Firefighting Water Reach in Dense Settlements With No Hydrants: A Tanker-Shuttle, Hose-Relay and Buffering Bound

A water-delivery model for dense settlements with no hydrants (SIMULATED, NOT MEASURED), combining a tanker shuttle cycle (7,500 litre tankers, 11.0 minute fixed allowance for filling, dumping and manoeuvring, road speeds of 30 km/h paved, 20 km/h gravel and 12 km/h on a poor track), Hazen-Williams hose friction with elevation, and portable-tank buffering. At a design flow of 1,000 litres per minute a source 2.0 km away on gravel has a 23.0 minute cycle and one tanker sustains 326.1 litres per minute, so 4 tankers sustain 1,304 litres per minute; a fleet of 4 reaches 4.75 km on paved roads, 3.17 km on gravel and 1.9 km on a track, falling to 0.9 km on a track at 1,500 litres per minute. In 70 mm hose at 1,000 litres per minute friction is 2.379 bar per 100 m, the maximum single-pump lay is 315 m on flat ground, and relay spacing is 252 m flat and 186 m at a 20 m rise; two 10,000 litre portable tanks buffer 20.0 minutes against a 5.75 minute tanker arrival interval. The costed design case protects 300 structures for $193,000, or $643 per protected structure. A single fill lane passes at most 1,250 litres per minute, so 1,500 litres per minute cannot be sustained at any fleet size through one lane, and beyond 3.4 km on a track even 6 tankers fail at the design flow, requiring static water points spaced at most 3.8 km apart on tracks, 6.33 km on gravel and 9.5 km on paved roads at $9,500 per point.