A Household Radio Tree for Emergency Alerts: Hop Range by Terrain, Relay Count, and Time to Alert a Settlement Without a Repeater

When mobile networks and mains power fail together, a settlement that owns handheld radios still owns a network, provided the radios are organised before the emergency rather than during it. This paper designs that organisation: a relay tree of households, each holding one 5 W handheld radio at 446 MHz, passing an alert outward from a central origin with no repeater, no mast, and no infrastructure. Under stated assumptions (transmit power 37.0 dBm, whip gain 1.5 dBi at each end, receiver sensitivity -120 dBm, a 10 dB fade margin, and so a largest workable path loss of 148.0 dB), the largest single hop is 7517.8 m over flat open ground, 2000.2 m over broken or hilly ground, and 1674.2 m through forest. Planning each hop at 0.8 of those figures, a settlement spread over a disc 8 km across with 503 households needs no relay household at all on flat ground, 18 relay households at a tree depth of 2 hops on broken ground, and 30 relay households at a depth of 3 hops in forest. With a stated calling protocol of 45 seconds per hop and branches transmitting in parallel, the whole settlement is alerted in 45 seconds on flat ground, 1.5 minutes on broken ground, and 2.25 minutes in forest. The full set of radios, one per household plus 5 percent spares, costs USD 20102; with relay antenna kits the forest tree, the most expensive case, costs USD 20522 in total, or USD 40.80 per household. SIMULATED, NOT MEASURED.