Storing Winter Ice for Summer: A Melt-Loss Bound and an Insulation Sizing Rule for a Small Ice House

Before mechanical refrigeration, communities that wanted ice in summer harvested it in winter and stored it in insulated ice houses, accepting that part of the harvest would melt. How large that part is, and how it depends on the size of the store and the thickness of its insulation, decides whether a small household or village store is worth building at all. This paper computes the melt loss from first principles for a cubic store filled with ice blocks, insulated with packed sawdust, held through a 120-day warm season at a mean outside temperature of 25 °C, with stated ground and door-opening losses added. The results show a strong size effect. A 1 m cube store (825 kg of ice) loses everything before the season ends at insulation thicknesses of 0.15 m and 0.30 m, and keeps only 14.3 percent of its mass even at 0.60 m. A 2 m cube at 0.30 m insulation keeps 27.9 percent. A 3 m cube at 0.30 m keeps 52.6 percent, a 4 m cube at 0.30 m keeps 64.7 percent, and a 5 m cube at 0.60 m keeps 85.8 percent. The corresponding sizing rule is stated as harvest per tonne surviving: from 6.99 tonnes harvested per tonne surviving for the smallest viable case down to 1.17 for the largest, thickest case, with 1.90 for the practical middle case of a 3 m store at 0.30 m insulation. Door openings alone melt 127.8 kg over the season regardless of store size, which by itself exceeds what a very small store can afford. The practical conclusion is that below roughly 2 m of internal side, a sawdust-insulated store of this design does not work as a season-long store, and that adding insulation and adding size are substitutes only within limits set out in the results.