Hello,

Does anyone have the math behind the equation 8" per mile squared?

I'm in a deep conversation about FE with an influential person in a church denomination. He is an engineer and loves math. I've been working with his equations — which he says debunk the Flat Earth. We haven't got to the actual observations yet. We are just trying to iron out the math.

His big equation deals with the calculation to find the distance to the horizon.

When I asked about the calculation of the earth's curvature — he was totally clueless — even though he is the "spokesperson" on the FE topic.

So I mentioned 8" per mile squared. At first, he didn't want to consider a calculation like this. I convinced him to try. He came up with 16" per mile squared — which totallly baffled me. Plus, it would only help the FE arguments.

But I told him I would look for the math behind the 8" per mile squared.

Can someone help me with the math?

Thanks.

One point: The horizon is 3 miles away for a 6 ft high person. 3 miles. That's not our math, that's theirs.

https://www.livescience.com/32111-how-far-away-is-the-horizon.html - (gotta love this article..."so in a particularly frosty location such as Antarctica people have been able to see hundreds of miles away.")

I'm calling DS (dinosaur sh**) on that. Wow. Refraction doesn't even approach the cilia hairs of being to compensate for that kind of distance, in Antarctica or anywhere else. Absolute bunk.

So when people are taking pictures of objects 10 miles, 20 miles, 65 miles, farther, and the army has line of sight weapons at 100 miles, (which they can only use on frosty days in Antarctica when the conditions are right), whales and submarines can communicate over 1000s of miles with sonar, submarines don't bother trying to hide behind the curvature of the earth because they can't, radio waves can be sent 1000s of miles across the ocean, etc etc, the fact is we can see too far. Period.

As for the actual math, give me a bit, and we can go over that as well.

The charts compare 4 different formulas for curvature, and you can see the difference between them is negligible.

I'm all over this! This is exactly what the turning point for me was, going home and doing the math. I'm shocked he isn't able to do it, as his level of math is even higher than mine. Sheesh....

I'll paste apic below that I have, where someone used several formulas and compared them all. I actually don't even like the phrase "8 inches per mile squared", because it is not good English for what the formula is. That phrase looks like "8/ mi^2", and that isn't what we do.

A better phrase is "8 inches x the square of the miles".

I think his problem may be that this formula is actually the equation of a parabola, not a circle. But it is still really accurate up to about 100 miles, which is more than sufficient.

Using the circumference and radius of the earth in the globe model, and just Pythagoras' Theorem, the numbers pop out fairly readily.