8 inches per miles-squared is only good over short distances... right?
Let's see how good it really is.
tl;dr: Attention Flat-Earth Debunkers! Stop saying 8 inches per miles-squared is only good over short distances. Stop saying 8 inches per miles-squared is a parabola. Instead, please focus on misuse of the approximation.
This was a really long video, so I plan to edit down a short version with just the results later.
-THE MATH ZONE-
@8:54 Deriving the correct drop formula based on arc length
@15:17 Deriving the correct drop formula based on horizontal distance
@18:46 Why are the equations so different? That's how we know math works
@22:16 Deriving the correct drop formula based on peak-to-peak distance
@24:19 Deriving the correct drop formula based on chord length
@25:34 4 different correct formulas for the curvature drop vs distance
@26:05 Comparison of drop heights vs the 8 inches per miles-squared
@29:40 The comparison in a spreadsheet (see below)
@31:24 The comparison as a graph
@33:08 8 inches per miles-squared is within 1% of the correct value all the way out to 1300 miles!
@33:37 Review of comment thread where a glober refuses to accept corrections.
"Silly Claims 04 - 8 inches per mile squared"
by AB science
Caught by TruthNerds
@18:46 Mistake: You misquoted your formula, it is 2r sin²(γ), not 2r sin²(α). Since γ = α/2, this gives 2r sin²(α/2), and only then we can use the trigonometric identity 2sin²(θ) = 1 - cos(2θ) to convert between the two versions.
- Flat Earth Explored