Empirical Earth · Shape, Curvature & the Horizon
The 8-inch rule, done right — a curve calculator
The claim
“8 inches per mile squared means distant things should vanish — but we still see them.”
What is measured
The famous 8-inches-per-mile² figure is the drop below a level line, not what a distant object loses behind the curve. Add your eye height and refraction, the way surveyors always have, and the “impossible” sightings line up with a 6,371 km ball. More on refraction and the curve.
What would show this is wrong
a sightline whose hidden height, worked out with the observer’s real eye height and standard refraction, does not match what is visible.
Sources
- Dip of the horizon. The visible horizon lies below true horizontal by θ = arccos(R/(R+h)); about 1° from a 1,000 m hill and ~3° at jet altitude, reduced ~8% by refraction. A standard celesti link
- Chicago across Lake Michigan. From the Michigan shore, roughly 53 to 59 miles across the lake, only the tallest Chicago towers clear the horizon on a normal day while the lower skyline stays link
- Dip of the horizon. The horizon sits below eye level by an angle that grows with the square root of observer height and is reduced a little by refraction, reaching about 3 degrees at airline link
- The Rainy Lake experiment. A controlled test over about 10 km used two rows of targets at known heights; the measured drop of the equal-height row matched a globe with terrestrial refraction link
- LIGO is engineered around Earth’s curvature. Each of LIGO’s two arms is a 4-kilometer laser beam in an ultra-high-vacuum steel tube. Because the beam travels straight while the Earth’s surfa link
The full entry, with the working →