Table of Contents
Globe vs Flat
The spherical Earth (R=6371 km) and flat earth models make different testable predictions. On a sphere, the surface curves away, creating a geometric horizon. Objects beyond it are progressively hidden bottom-first. On a flat plane, there would be no geometric horizon. This calculator computes curvature predictions that can be verified with basic surveying equipment.
At 1.7 m eye height, the horizon is about 4.65 km away. At 10 km distance, about 7.85 m of an object is hidden by curvature. These predictions are consistently confirmed by observations of ships disappearing hull-first, city skylines partially hidden by curvature, and careful laser/theodolite measurements.
Formulas
Evidence
| Height | Horizon | Drop at 10km |
|---|---|---|
| 1.7 m | 4.65 km | 7.85 m |
| 10 m | 11.3 km | 7.85 m |
| 100 m | 35.7 km | 7.85 m |
| 10 km | 357 km | 7.85 m |
FAQ
Can you see curvature?
Individual drop is small at short range (~8 cm/km). But the horizon effect is easily observed: ships disappear bottom-first, and the order of disappearance matches spherical geometry predictions precisely. High-altitude photography clearly shows Earth's curved limb.
What about refraction?
Atmospheric refraction bends light around the curve, letting you see ~8% farther than geometric predictions. Standard refraction uses effective radius 7/6*R. Unusual conditions create mirages (superior and inferior) that can make objects briefly visible beyond the normal horizon.
Has curvature been directly measured?
Yes, countless times. Bedford Level experiment (1870), geodetic surveys worldwide, GPS satellite networks, laser gyroscopes, Foucault pendulums, and direct photography from space all confirm Earth's spherical shape with radius ~6,371 km.