A Winter Stores Bound for the Honey Bee Hive: Insulation, Heat Loss, and the Honey a Colony Must Spend

A clustered honey bee colony in winter is, in thermal terms, a small heat source inside a thin wooden box, and the honey it eats is the fuel that pays for the heat the box loses. This study computes an upper bound on that fuel bill. A two-box hive is modelled as a set of conducting surfaces with stated thermal transmittances, its cavity air is held at 10.0 degrees Celsius throughout a 150-day winter, and the heat crossing the walls, roof, and floor is converted into honey at 13.0 megajoules per kilogram with a conversion efficiency of 0.85. Two climates are examined: a cold continental winter with a mean temperature of -6.83 degrees Celsius and a mild maritime winter with a mean of 5.59 degrees Celsius. In the cold case the bound gives 73.16 kilograms of honey for an uninsulated hive built from 19 millimetre pine, 29.99 kilograms with 25 millimetres of added expanded polystyrene, and 22.17 kilograms with 50 millimetres, a reduction of 69.7 percent. In the mild case the corresponding figures are 19.16, 7.85, and 5.81 kilograms. Insulating the roof alone barely helps, leaving a cold-winter bound of 64.25 kilograms, because the walls dominate the loss. Once walls and roof are insulated, the uninsulated floor becomes the largest single remaining path. The sizing rule that follows is stated as a conductance limit: to hold the cold-winter bound at or below 20 kilograms, the whole-hive conductance must not exceed 1.013 watts per kelvin, which among the constructions tested requires 100 millimetres of expanded polystyrene or 50 millimetres of polyisocyanurate on walls and roof. The absolute values are bounds under a deliberately demanding held-cavity assumption and overstate the consumption of colonies whose cavity air is allowed to drift downward; the ratios between constructions and the conductance threshold are the durable results. This study is simulated, not measured.