Summer Heat Load in the Honey Bee Hive: Fanning Bees, Water Demand, and a Roof and Shade Sizing Rule

In summer the thermal problem of a hive reverses: the colony must dispose of heat rather than conserve it, and it pays for cooling in water fetched by foragers and in bees diverted to fanning. This study computes that bill for a two-box hive under stated solar and temperature conditions. With a roof irradiance of 850 watts per square metre and sunlit walls at 450 watts per square metre, the solar heat conducted into an uninsulated hive is 44.9 watts under white paint, 82.3 watts under weathered pine, and 127.1 watts under a dark finish. At an ambient temperature of 43 degrees Celsius the resulting evaporative cooling load is 102.5 watts for the white hive and 184.7 watts for the dark hive, requiring 151.8 grams of water per hour and 186 fanning bees in the first case and 273.7 grams per hour and 336 fanning bees in the second. Full shade lowers the load at the same temperature to 57.6 watts, 85.3 grams per hour, and 105 fanning bees. Two negative results are as important as the positive ones. First, the fanning force never approaches the examined threshold of 10 percent of a 10000-bee forager force: the largest computed commitment is 336 bees, which is 3.4 percent. Water, not bee numbers, is the binding constraint, with a dark hive needing 1642.0 grams of water across a 6-hour hot window at 43 degrees Celsius. Second, a target of holding water demand at or below 80 grams per hour at 43 degrees Celsius cannot be met by any roof colour, because even full shade leaves a load of 57.6 watts against the 54.0 watts that the target permits, the remainder being metabolic and conducted heat that paint cannot remove. Hive volume, finally, provides almost no thermal buffer: the air in one, two, and three boxes stores only 0.24, 0.49, and 0.73 kilojoules per 5 degrees of warming. The sizing rule is therefore about surfaces, not volume: use a light roof, insulate the roof, and shade the hive where possible, in that order of preference where all three cannot be had. This study is simulated, not measured.