Wax Rendering, Weighed Honestly: Mass Balance, Method Losses, and a Solar Melter Sizing Rule

Rendering beeswax is usually discussed in the language of craft habit rather than arithmetic, and one habit in particular has survived for decades: the claim that old brood comb renders about half its weight in clean wax. This paper tests that claim and the wider rendering question with an explicit mass balance. Four classes of input are defined by their wax mass fraction, from cappings at 0.92 to old brood comb at 0.32, with the remainder assigned to cocoon silk, pollen, propolis and debris. Two rendering methods are compared, a hot water bath and a solar melter, each with its own fraction of contained wax released and a common handling loss. The computed yield of clean wax in a water bath is 0.8565 kg per kilogram of cappings but only 0.2132 kg per kilogram of old brood comb, and in a solar melter the old-comb yield falls further to 0.1725 kg per kilogram. Even with a second pressing of the bath residue, old brood comb yields 0.2484 kg per kilogram. The belief that old comb renders about half wax therefore does not survive the arithmetic: the water-bath yield is only 0.4264 of the claimed half. A two-bound sizing method for solar melters is also derived, in which an energy bound and a tray loading bound are computed separately and the smaller governs. For the stated reference harvest of 500 kg of honey producing 12 kg of drained cappings, the recommended solar melter area, including a margin, is 2.5 square metres. Washing drained cappings recovers 0.153 kg of honey per kilogram of cappings, or 1.836 kg across the reference harvest. This study is simulated, not measured: every number follows from the stated assumptions by the accompanying computation, and no rendering trial was performed.