# Coverage Radius Estimation by Terrain Type ## The Radio Horizon Formula The theoretical radio horizon for a single antenna at height *h* metres above a smooth spherical earth, accounting for standard atmospheric refraction (the 4/3-earth model), is: ``` d (km) = 4.12 × √h_m (radio horizon, 4/3-earth refraction) ``` For a link between two antennas at heights h₁ and h₂ the total radio horizon is: ``` d_total (km) = 4.12 × (√h₁ + √h₂) ``` Note: the purely geometric (optical) line-of-sight horizon uses the coefficient 3.57 × √h. The 4.12 coefficient adds the standard 4/3-earth refraction correction and is the value used for *radio* horizon throughout this book (consistent with the mountain-and-complex-terrain and repeater-placement pages). There is no latitude term in this formula. This is the *maximum possible* range on a flat, unobstructed earth - a theoretical ceiling, not a usable-coverage promise. Real terrain, vegetation, and buildings reduce this significantly. The formula provides the ceiling; terrain obstruction factors bring it down to a realistic estimate. --- ## Terrain Obstruction Factors Apply these multipliers to the radio-horizon distance to get a realistic coverage radius. The factor bands below are *illustrative planning heuristics*, not measured constants - no Tier-1 standard assigns these exact multipliers to named terrain classes. The underlying propagation behaviour is described in ITU-R P.526 (diffraction), P.833 (vegetation), and P.1411 (urban/suburban short-range); use those for rigorous modelling.
Environment Type Obstruction Factor Effective Coverage (%) Notes
Flat open (farmland, desert, water) 0.85 - 1.00 85 - 100% Near-theoretical range; ground reflections can help at low angles
Gentle rolling terrain 0.65 - 0.80 65 - 80% Moderate ridge shadowing; elevated repeaters mitigate well
Suburban (low-rise, gardens) 0.50 - 0.65 50 - 65% Houses and trees add 5 - 15 dB of excess loss (ITU-R P.1411 range)
Dense forest / jungle 0.35 - 0.55 35 - 55% Vegetation loss ~0.2 - 0.5 dB/m through canopy at 915 MHz (ITU-R P.833 / Weissberger); saturates beyond ~14 m depth
Urban (mid-rise, 3 - 8 floors) 0.30 - 0.50 30 - 50% Building diffraction dominates; rooftop-to-rooftop paths much better
Dense urban (high-rise, canyons) 0.15 - 0.30 15 - 30% Multipath + shadowing severe; per-block coverage planning needed
Mountainous / complex terrain 0.20 - 0.60 20 - 60% Highly variable; valleys may have near-zero coverage from a single site
--- ## Worked Examples The coverage *areas* below are theoretical maxima derived from the radio-horizon ceiling times an obstruction factor. They are **not** the usable coverage you should plan around. In practice a single well-placed repeater at ~30 m AGL delivers on the order of **300 - 800 km²** of reliable coverage in flat/rolling terrain, and far less in forest or urban settings - see the repeater-placement-principles and repeater-grid pages for realistic per-terrain planning densities. Treat the figures here as "maximum, not expected." ### Example 1 - 30 m Tower on Flat Land A community group installs a repeater at the top of a 30 m self-supporting tower in flat agricultural land. The mobile clients they serve have antennas at 1.5 m AGL. ``` Radio horizon (tower): 4.12 × √30 = 4.12 × 5.48 = 22.6 km Radio horizon (client): 4.12 × √1.5 = 4.12 × 1.22 = 5.0 km Total radio horizon: 22.6 + 5.0 = 27.6 km Obstruction factor (flat open): 0.90 Theoretical coverage radius: 27.6 × 0.90 ≈ 24.8 km Theoretical coverage area (ceiling): π × 24.8² ≈ 1,930 km² ``` That ~1,930 km² is the radio-horizon ceiling, not a usable-coverage guarantee. Realistic usable coverage from a single well-sited rural tower is far lower - typically on the order of 300 - 800 km² once real-world fading, foliage, and link-margin requirements are accounted for. Plan around the usable figure, not the ceiling. ### Example 2 - 10 m Mast in Suburbs A volunteer mounts a repeater on a 10 m mast attached to their house in a typical American suburb (one-storey houses, trees). Mobile clients at 1.5 m. ``` Radio horizon (mast): 4.12 × √10 = 4.12 × 3.16 = 13.0 km Radio horizon (client): 4.12 × √1.5 = 4.12 × 1.22 = 5.0 km Total radio horizon: 13.0 + 5.0 = 18.0 km Obstruction factor (suburban): 0.55 Theoretical coverage radius: 18.0 × 0.55 ≈ 9.9 km Theoretical coverage area (ceiling): π × 9.9² ≈ 308 km² ``` This is a solid community repeater covering roughly the footprint of a small city, though the 308 km² figure is again a ceiling - expect meaningfully less usable coverage. Pockets of shadow behind larger buildings will exist. A wardriving survey is recommended after installation to confirm actual coverage. ### Example 3 - Rooftop in Dense Urban A repeater is placed on the flat roof of a 7-storey (21 m) apartment building in a dense city. Surrounding buildings average 6 storeys (18 m). Mobile clients at street level (1.5 m). ``` Radio horizon (roof): 4.12 × √21 = 4.12 × 4.58 = 18.9 km Radio horizon (client): 4.12 × √1.5 = 4.12 × 1.22 = 5.0 km Total radio horizon: 18.9 + 5.0 = 23.9 km Obstruction factor (dense urban): 0.25 Theoretical coverage radius: 23.9 × 0.25 ≈ 6.0 km Theoretical coverage area (ceiling): π × 6.0² ≈ 113 km² ``` Only 25% of the theoretical range is realised because the repeater barely clears the surrounding roofline. Raising the antenna by 3 additional storeys (to 30 m) lifts the horizon to ~27.6 km and, at an improved ~0.35 obstruction factor, the ceiling rises to a radius of ~9.7 km - roughly π × 9.7² ≈ 295 km² (still a theoretical maximum, with usable coverage well below that). In dense urban networks, rooftop height relative to surroundings matters enormously. --- ## Coverage Overlap: The 20 - 30% Rule When planning adjacent repeaters, their coverage footprints should overlap by 20 - 30% of the coverage radius. This is a rule of thumb borrowed from cellular and WLAN cell-planning practice (which commonly calls for 15 - 30% overlap). It ensures: - No gap corridor between repeaters where nodes lose connectivity - Sufficient signal margin at the cell edge for reliable forwarding (not just barely detectable signals) - Redundancy: a node in the overlap zone can reach two repeaters If repeater A has a coverage radius of 8 km and repeater B also has 8 km, place the two sites about 12 - 13 km apart to keep ~20 - 30% overlap (a single shared lens-shaped zone roughly 3 - 4 km wide in the middle - not "on each side"). At exactly 16 km the two cells are tangent: they just touch, with zero overlap margin and zero gap. Only beyond ~16 - 18 km does a real gap corridor open up where nodes may lose both repeaters. --- ## Link Budget Margin: Target >10 dB Coverage radius estimates are not hard boundaries - they define the distance at which the link margin drops to zero. In practice, a link operating at exactly the sensitivity floor is unreliable. Fading, multipath, vegetation sway, and atmospheric changes will cause it to fail intermittently. **Target at least 10 dB of margin at the cell edge** for reliable operation. This means planning for a coverage radius at which the received signal is 10 dB above the receiver sensitivity floor. The 10 dB figure is a standard engineering convention (see any link-budget reference); the margin you actually need scales with the environment - budget more in heavy-fading or foliage-dense paths. For Meshtastic on SF12 / BW125 (the Long Slow preset), receiver sensitivity is approximately −137 dBm with the SX1262's *Rx Boosted* gain enabled (standard gain is ~3 - 4 dB worse). Note that LongFast (SF11 / BW250) has a sensitivity closer to −131 dBm, not −137. A link budget target of −127 dBm at the coverage boundary gives 10 dB of margin relative to the SF12/BW125 floor. Links measured below −127 dBm at normal operating distances should be treated as marginal and either reinforced with a relay node or deprioritised until a better repeater site is available. Quick field check: If a node reports RSSI < −125 dBm or SNR < −10 dB when communicating with its nearest repeater, that link is at or below the 10 dB margin boundary. Plan to add a relay or move the repeater closer.