Frost Protection Priced in Water and Heat: Sprinklers, Fires, and Covers Against a Radiation Frost

Three remedies are commonly offered when a radiation frost threatens a small plot: run sprinklers, light fires, or cover the crop. This paper prices all three against a stated base case — a clear, calm night with a canopy heat loss of 75 W/m2, air falling to −3 °C, and six hours at or below freezing — using stated assumptions throughout. Sprinkler protection, which holds tissue at 0 °C with the latent heat released as water freezes on the plant, requires 1.01 mm/h in the calm base case, or 60.6 m3 of water per hectare over six hours (80.8 m3 over eight hours); under a wind and evaporation penalty the requirement rises to 2.91 mm/h and 174.6 m3 per hectare over six hours, and sprinkling can harm when evaporation cools wet tissue before a freezing layer is established. Small fires fail the arithmetic outright at customary densities: 50 fires per hectare, at a generous stated 15 kW each with a quarter of the heat delivered to the crop layer, supply only 18.8 W/m2 against the 75 W/m2 loss, and matching the loss would take about 200 fires per hectare. A stated fleece cover, cutting radiative loss by 55%, holds tissue about 2.0 °C above unprotected tissue — genuine but partial protection that does not by itself cover the full stated frost. The practical rule is: cover first for shallow frosts, sprinkle where water and calm air allow, and do not rely on a ring of small fires. This study is simulated, not measured.