Radio Path Profile: Mountain Relay Fresnel Clearance

Relay Chain

Relay drones 3

Terrain ruggedness 1.0×

Radio frequency 2.40 GHz

Transmit power 1.0×

Placement mode

Link Status

Signal at search drone

—

Chain status

—

Worst Fresnel-zone clearance

—

Path length (chain vs. direct)

—

How it works

This is a radio path profile — the exact 2D vertical cross-section real RF engineers plot to plan a mountain link: horizontal distance on x, altitude in metres on y. Free-space received power still falls off with the inverse-square law relative to a reference distance d₀ set by the transmit-power slider:

S(d) = 100 × (d₀ / d)² × 10^(−L_diff/10)   (clamped to [0, 100]%)

Unlike a simple "blocked or not" check, real radio waves bend around obstacles (diffraction). What matters is not just whether the ground pokes above the straight line between two antennas, but how far it intrudes into the first Fresnel zone — an ellipse of radius

F₁ = √(λ·d₁·d₂ / D)          D = d₁+d₂, λ = c/frequency

around that line. Every hop is scanned for its worst obstruction and converted into the Fresnel-Kirchhoff diffraction parameter ν, then into extra path loss via the standard single-knife-edge approximation (ITU-R P.526 / Lee 1985):

ν = h·√(2D / (λ·d₁·d₂))            h = height of terrain above the direct line
L(ν) ≈ 0 dB                         ν ≤ −1   (clear, ≥ full 1st Fresnel zone)
L(ν) ≈ 6 dB                         ν = 0    (grazing incidence — top of ridge on the line)
L(ν) grows further                  ν > 0    (ridge intrudes into the beam)

Relay drones — more relays means shorter, stronger hops, but each is one more link a ridge can intrude on.
Terrain ruggedness — taller peaks are more likely to eat into a hop's Fresnel zone.
Radio frequency — shorter wavelengths (higher GHz) diffract less around obstacles, so the same ridge costs more dB at 5.8 GHz than at 900 MHz — a real, distinctly 2D-profile effect this simulation lets you feel directly.
Transmit power — a stronger radio raises d₀, so every hop reads a higher percentage before it degrades.
Terrain-following vs. naive placement — the smart mode holds each relay at a fixed clearance above the ridge directly beneath it; the naive mode linearly interpolates altitude in a straight line from base to drone, which dips toward valleys and skims far more ridgelines.

The shaded band around each link is the actual first Fresnel-zone ellipse — watch it visibly pinch against the terrain as a hop degrades, instead of a link simply switching off.

Base station Relay drone Search drone Link — clear Link — degraded Link — lost