Fresnel Clearance: Radius, Antenna Height, and Deployment Cost
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.
See the relationship before changing it
Set the input, apply the rule, then read the result with its unit.
The retained audit below checks several chapter fixtures. This model keeps those stated values fixed and changes only wi-fi path length, so the numeric fixture does not switch without explanation.
Derive the baseline in four named moves
- 1
Name the input. The chapter baseline is 100 m.
- 2
Name the relationship. clearance = 0.6 x 17.3 x sqrt((distance / 1,000) / (4 x 2.4))
- 3
Substitute with units. 0.6 x 17.3 x sqrt(0.100 km / (4 x 2.4 GHz)) = 1.06 m
- 4
Read the result. Keep the unit beside the value. Use it only inside the technical boundary on this page.
Predict, then change wi-fi path length
Try Predict the direction of clearance = 0.6 x 17.3 x sqrt((distance / 1,000) / (4 x 2.4)). Test another wi-fi path length, then compare required fresnel clearance.
Observe A longer path widens the first Fresnel zone when frequency and the midpoint split stay fixed. Reset wi-fi path length to 100 and compare required fresnel clearance.
Explain A longer radio path broadens the region where reflected waves can interfere, so the required Fresnel clearance grows with the square root of path length.
Check yourself
What should you do before trusting a moved-control result?
What does this small model leave out?
Ready: use the stated baseline inputs, then compare each displayed result.
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.