Rooftop Water Storage and Heat Co-Design for Apartment Blocks: A Coupled Sizing Rule Bounded by Roof Load

SIMULATED, NOT MEASURED. A rooftop rainwater/greywater tank is sized jointly as emergency water storage and as a thermal buffer and shading mass for top-floor flats, with the structural roof-load bound as the binding constraint. For a representative block with a 360 m2 roof, 24 flats and 60 residents, storage is expressed as s in litres per square metre of roof; at an emergency demand of 50 litres per person per day each 1 L/m2 buys 2.88 hours of whole-block autonomy. On a typical existing reinforced-concrete roof (allowable added load 75 kg/m2, tank dead load 10 kg/m2) the bound is s = 65 L/m2: a 23,400-litre tank at 108.3 mm depth over 0.60 of the roof, providing 187.2 hours (7.8 days) of emergency autonomy (62.4 hours at normal demand) and, in a lumped thermal simulation of a repeating 38 C / 26 C heatwave, cutting the top-floor peak from 41.81 C to 39.06 C, a reduction of 2.75 C (an average of 0.423 C per 10 L/m2), delaying crossing of 32 C from 19.75 to 37.7 hours, at $34,930 per block or $1,455.42 per flat ($1.493 per litre). On a strong or new roof the bound is 140 L/m2, 403.2 hours and a 4.58 C reduction at $2,524.17 per flat. The design fails on light or legacy roofs: the bound is only 15 L/m2, 5,400 litres, 43.2 hours of autonomy, below the 72-hour usefulness threshold, at the highest unit cost of $3.302 per litre; the minimum useful storage is 25 L/m2, requiring an allowable added load of at least 35 kg/m2, below which ground-level storage plus separate lightweight roof treatment is the correct design. Rain alone fills the typical tank from empty in 37.1 days at 631.2 litres per day average capture, and in no modelled case does the tank alone keep the top floor below 32 C.