The Earth's curvature is typically expressed in terms of drop per distance, radius of curvature, or sagitta (chord height difference). Here are a few ways it's quantified:
1. Drop Over Distance
A common approximation is:
Over 1 mile (1.61 km), the Earth's surface drops about 8 inches (20 cm).
Over 10 miles (16.1 km), the drop is about 66.7 feet (20.3 m).
Over 100 miles (161 km), the drop is about 6,667 feet (2,032 m).
The formula for the drop d due to curvature over a distance x on a sphere of radius R is:
d=R−R2−x2
For Earth, where R ≈ 3,959 miles (6,371 km), you can compute the drop for any distance.
2. Radius of Curvature
The Earth's mean radius is 6,371 km (3,959 miles). This value is used in many geophysical and engineering calculations.
3. Sagitta (Height of Arc Over a Chord)
If you draw a straight line (chord) between two points on Earth's surface, the maximum height h of Earth's curvature above the chord is given by:
h=x22R
where x is half the chord length.
Would you like a specific calculation for a given distance?