Also known as: refraction, atmospheric refraction

Refraction is the bending of a radio wave’s path as it travels through a medium whose refractive index changes with position.¹ In the atmosphere, air density, pressure, temperature, and humidity normally decrease with altitude, so the refractive index falls with height and radio rays curve gently downward, following the Earth’s curvature and reaching slightly farther than a straight line would. This is why the radio horizon is a little beyond the visual horizon.

The refracted radio ray curves downward, reaching beyond the straight-line optical horizon.

How it works

By Snell’s law, a wave crossing between regions of differing refractive index changes direction; a continuous gradient bends it along a smooth curve. Two ways of quantifying atmospheric refraction are standard:

• Refractivity gradient. The refractive index of air is only slightly above 1, so engineers work with refractivity N = (n − 1)·10⁶. Its rate of decrease with height sets how sharply rays bend.
• The k-factor (effective Earth radius). Rather than track curved rays over a curved Earth, the geometry is flattened by pretending the Earth has an inflated radius k·R and letting the rays travel straight. Standard atmosphere gives k = 4/3, the familiar “four-thirds Earth” that extends the horizon by about 15% versus the geometric value.

Conditions that steepen the gradient bend rays harder. A strong temperature inversion can push k very high or even trap rays in a tropospheric duct, carrying VHF/UHF signals hundreds of kilometres. A sub-standard gradient (k < 1) bends rays upward, shortening the horizon and even blocking paths that normally close.

Variants

Refraction operates at every layer. In the troposphere it is the mild, ever-present bending described above. In the ionosphere the mechanism is far stronger: free electrons make the refractive index depend on frequency, bending HF waves so sharply they return to Earth — the basis of long-distance shortwave propagation. The same physics, applied to light, is what makes a spoon look bent in a glass of water.

Relevance to SDR

For a scanner, tropospheric refraction is the everyday reason coverage reaches a bit past line-of-sight. The k = 4/3 model is baked into how coverage maps and radio-horizon calculators estimate range for a given antenna height, so a trunking site reliably serves users somewhat beyond the geometric horizon. When the weather sets up a strong inversion, enhanced refraction and ducting can briefly deliver distant VHF/UHF systems from far outside the normal service area — a familiar “band opening” for hobbyists.

Refraction also subtly shifts the apparent elevation of satellites near the horizon, a correction that precise GNSS and satellite-tracking receivers account for. GopherTrunk does no propagation modelling itself; refraction is a property of the channel that changes which signals arrive at the antenna, not something the decoder computes.

In practice

The single most useful takeaway is the four-thirds-Earth rule: it lets a planner treat rays as straight while still crediting the extra range refraction provides, and it pairs with knife-edge diffraction and Fresnel-zone clearance to predict real coverage over terrain.

Sources

1. Atmospheric refraction — Wikipedia, on the downward bending of rays, the refractivity gradient, and the effective-Earth-radius model. ↩

See also

• Radio horizon
• Tropospheric ducting
• Knife-edge diffraction
• Ionospheric propagation
• Radio propagation