The old Bedfordshire level experiment.
A boat carrying a flag rode from one bridge to another over 6 miles of level, canal water, which should be 16 feet below the observer sight line at that distance, if we used standard accepted curvature formula.
The observer with a telescope was just 18 inches above the water level.
FORMULA:
(Take from Google Gemeni AI)
The standard rule of thumb used for estimating the earth’s geometric curvature is 8 inches per mile squared ($8 \text{ in/mi}^2$).
Because the Earth is a sphere, with a generally accepted radius of about 3,900 miles, the drop in surface elevation isn’t a constant linear rate—it increases exponentially with distance.
How the Rule Works
To calculate the total geometric drop over a given distance, you take the distance in miles, square it, and multiply by 8 inches:
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1 Mile: $1^2 \times 8 = \mathbf{8 \text{ inches}}$
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2 Miles: $2^2 \times 8 = \mathbf{32 \text{ inches}}$ (~2.6 feet)
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3 Miles: $3^2 \times 8 = \mathbf{72 \text{ inches}}$ (6 feet)
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10 Miles: $10^2 \times 8 = \mathbf{800 \text{ inches}}$ (~66.7 feet)
Note on Practical Viewing:
This formula calculates geometric curvature from a point tangent to the surface. It does not account for line-of-sight visual effects like atmospheric refraction (which slightly bends light rays along the surface, allowing you to see roughly 8–14% farther than purely geometric math predicts) or observer eye-level elevation.