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 true

The 8-inches-per-mile² figure is real arithmetic and gives exactly the number it claims to give.

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 an Earth of 6,371 km radius. 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

  1. 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
  2. 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
  3. 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
  4. 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
  5. 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
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