Sagitta is the fancy term for what is commonly referred to in flat vs. globe discussions as "the bulge."

I've always been a bit annoyed by references to "the bulge" in talking about "globe earth theory;" and not because of the term itself but because I don't think the measure of the arc above the chord is germane. The bulge is not a mound or hill that rises up in front of you on a globe and presenting an obstacle. The bulge is not the obstacle. The horizon is.

The only time that the bulge matters is when the horizon happens to coincide with it, as I've depicted with the diagram (from Metabunk's interactive visualizer) above. The horizon is a function of height above the arc. The bulge is a function of base locations on the arc. For any two points on the arc of a globe, the obstructing horizon varies with height but the bulge is fixed. Only at a height where the horizon corresponds to the midpoint on the arc between two points does the bulge matter, and then only because it's where the horizon is.

The "bulge" isn't a mound rising before your eyes. On a globe, the arcing surface drops away from your eye level. If I had my druthers, we'd banish "the bulge" from any discussion about how things work on a globe. It's often misconstrued and misrepresented as that which causes or would cause an obstruction to line of sight compared to a flat earth; but that's in error.

Consider two points on earth that are 30 miles apart.

On a flat surface, they're just that: 30 miles apart.

On a globe with a radius of 3959 miles, they are 30 miles apart on an arc of 0.43°. The height of that arc above a straight line (chord) between those two points -- that height being the bulge or sagitta -- is 0.0284 miles or 150 feet. Over the span of 158,400' between the two points on the arc, how significant is that 150' sagitta?

That additional 150' of the sagitta (bulge) contributes some amount of additional distance on the arc of a globe compared to the straight line chord length which would be the flat earth distance. Guess how much extra distance? Or, if you know how to do the math, work it out.

I'll be back.

Edit: Come on, my fellow globelings. This question is for anyone, and I'm sure globe supporters can come up with the solution. There's probably even an online calculator that can provide the number.

But until then, just guess. Anyone? What do you think the difference is between arc length and chord length in the 30-mile distance scenario above that a 150' "bulge" would produce? Just ballpark it.