Fresnel zones: more than line of sight

More than a thin ray

Obstacles can affect a radio path even when the direct line of sight just remains clear. Fresnel zones describe locations with equal extra path length relative to the direct path. The first-zone radius is approximately r₁ = √(λ·d₁·d₂/(d₁+d₂)). The two distances refer to the point being examined along the path.

For a fixed total path length, radius is largest at the midpoint and decreases towards the ends. For 10 km at 435 MHz, midpoint radius is about 41.5 m. At higher frequency the zone becomes smaller for the same geometry because wavelength decreases.

60 percent is a planning measure

A clear region of at least roughly 60% of the first radius is commonly used as a planning rule. In this example it is about 24.9 m around the direct line at mid-path. This is not an elevation above sea level and does not guarantee a particular reception quality.

Assessing an obstacle requires the actual line-of-sight height at its position and the obstacle’s height. Longer paths also involve Earth curvature and atmospheric refraction. A radius calculator without a terrain profile can describe the required space but cannot confirm available clearance.

A useful comparison

Calculate the midpoint first, then a critical position near an endpoint. Keep total length constant by dividing d₁ and d₂ appropriately. Next compare two frequencies. This shows why the same tree can matter differently at different positions or on different bands.