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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 is: 

d (km) = 3.57 × √h_m
d_total (km) = 3.57 × (√h₁ + √h₂)

This is the maximum possible range on a flat, unobstructed earth. 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:

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
Dense forest / jungle 0.35 - 0.55 35 - 55% Vegetation loss: 0.2 - 0.4 dB/m through canopy at 915 MHz
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

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): 3.57 × √30 = 3.57 × 5.48 = 19.6 km
Radio horizon (client): 3.57 × √1.5 = 3.57 × 1.22 = 4.4 km
Total radio horizon: 19.6 + 4.4 = 24.0 km

Obstruction factor (flat open): 0.90

Realistic coverage radius: 24.0 × 0.90 ≈ 21.6 km
Coverage area: π × 21.6² ≈ 1,466 km²

With a single well-sited tower, this repeater comfortably covers a circle of about 1,500 km² - roughly the size of a mid-sized US county.

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): 3.57 × √10 = 3.57 × 3.16 = 11.3 km
Radio horizon (client): 3.57 × √1.5 = 3.57 × 1.22 = 4.4 km
Total radio horizon: 11.3 + 4.4 = 15.7 km

Obstruction factor (suburban): 0.55

Realistic coverage radius: 15.7 × 0.55 ≈ 8.6 km
Coverage area: π × 8.6² ≈ 232 km²

This is a solid community repeater covering roughly the footprint of a small city. However, 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): 3.57 × √21 = 3.57 × 4.58 = 16.4 km
Radio horizon (client): 3.57 × √1.5 = 3.57 × 1.22 = 4.4 km
Total radio horizon: 16.4 + 4.4 = 20.8 km

Obstruction factor (dense urban): 0.25

Realistic coverage radius: 20.8 × 0.25 ≈ 5.2 km
Coverage area: π × 5.2² ≈ 85 km²

Only 25% of the theoretical range is realised because the repeater barely clears the surrounding roofline. Even 3 additional storeys of height (to 30 m) would raise the obstruction factor to ~0.35 and expand coverage to ~120 km². 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 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 no more than 13 - 14 km apart (leaving 2 - 3 km of overlap on each side). Placing them 16 km apart creates a 0 - 2 km gap corridor in the middle where nodes may lose one or 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.

For Meshtastic on SF12 / BW125, receiver sensitivity is approximately −137 dBm. A link budget target of −127 dBm at the coverage boundary gives 10 dB margin. 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.

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