Curvature & Refraction

Understanding the subtle bending of light and Earth in precise surveying.

The Theory

Earth's Curvature ($h_c$)

A level surface follows the Earth's shape. A surveyor's horizontal line of sight departs from this level surface as distance increases.

$$h_c = 0.0785 K^2$$

Atmospheric Refraction ($h_r$)

Light bends downwards through the atmosphere, partially offsetting the effect of Earth's curvature. It's roughly 14% of the curvature correction.

$$h_r = 0.011 K^2$$

Combined Correction ($h_{cr}$)

The net difference between curvature and refraction that must be applied to precise leveling.

$$h_{cr} = h_c - h_r = 0.0675 K^2$$

K = Distance (km)  |  h = Correction (m)

Visual Diagram Not to scale
Level Surface (Earth) Rod Horizontal Line of Sight Refracted Path hc hr hcr

Correction Calculator

Kilometers