How to Use 8 Inches Per Mile Squared to Estimate the Hump Correctly
7Flat Earthers get confused with the formula thinking that it describes the hump of Earth between them and whatever they're looking at, but that's wrong. It's the drop - how much Earth's curvature drops away from a tangent to the surface, but that means it's also a sagitta for the segment that the observer is on "top" of.
The distance the flat Earther gives you is only half the arc length for this segment, since the other half is behind them, and the sagitta they're estimating isn't the one between them and the point of interest. It's the one for the segment they're on "top" of.
Globe proponents incorrectly dismiss this estimate as becoming too inaccurate over a few hundred miles, but that is false, as shown here. It's being misused. That's what the problem is. The formula estimates a sagitta very well if you understand how it works.
To use the formula to estimate the sagitta for the hump between the observer at sea level and the base of the point of interest also at sea level, moving halfway along that arc length to get to that sagitta.
Work out the distance from that point to the point of interest. It's half the distance the flat Earther quoted.
Then use the formula.
In short, it's 8 inches per miles halved squared, or 8*(0.5L)^2 in inches, or (8*(0.5L)^2)/12 in feet, or (8*(0.5L)^2)/(5280*12) in miles, where L is the distance to the point of interest.
Apologies for the sound. I'm using the laptop mic after the PC PSU failed.