Fresnel Clearance: Radius, Antenna Height, and Deployment Cost
Ada re-derives the chapter’s Fresnel radius, required clearance, mast height, and the deployment cost the geometry unlocks
ADA · CALCULATION AUDIT
Fresnel Clearance: Radius, Antenna Height, and Deployment Cost
Fresnel planning is geometry with a radio consequence: first calculate the invisible clearance envelope, then ask whether the antenna height really leaves enough of it open. The chapter’s own examples run a 100 m Wi-Fi bridge at 2.4 GHz and a 5 km LoRa link at 915 MHz, then turn the required clearance into a mast height and a deployment cost.
Companion to the chapter Fresnel Zones and Deployment — every number here comes from that chapter.
The clearance ledger
| Check | Arithmetic shown | Result | Design meaning |
|---|---|---|---|
| 100 m Wi-Fi bridge at 2.4 GHz | 17.3 * sqrt(0.1 / (4 * 2.4)) = 17.3 * sqrt(0.0104) | r1 = 1.77 m; 0.6 * 1.77 = 1.06 m | The short Wi-Fi link only needs about one meter of midpoint clearance before installation margin. |
| 5 km LoRa link at 915 MHz | 17.3 * sqrt(5 / (4 * 0.915)) = 17.3 * sqrt(1.366) | r1 = 20.22 m; 0.6 * 20.22 = 12.13 m | The long low-frequency link needs a much taller clearance envelope. |
| Gateway above 2 m crops | 2 + 12.13 = 14.13 m; round to a 15 m mast | (15 - 2) / 20.22 = 64.3% clear | The 15 m gateway clears the 60% rule; a 3 m gateway gives only (3 - 2) / 20.22 = 4.9%. |
| Infrastructure comparison | Ground: 39 * $1,500 = $58,500; tower: 4 * $1,500 + 4 * $3,000 = $18,000 | ($58,500 - $18,000) / $58,500 = 69.2% | The physics calculation explains why the taller design is cheaper despite the tower cost. |
Audit rule: do not copy a range claim forward unless the distance, frequency units, obstacle height, and clearance percentage are written beside the decision.
Every number above is taken from the chapter’s own Fresnel-zone worked examples and re-derived step by step.