Population Arithmetic and the Supering Rule: When Storage Binds and What a Week of Delay Costs

When to add a honey super is one of the oldest judgement calls in beekeeping, and it is usually made by looking at how full the top box appears. This study replaces the glance with arithmetic. The study is simulated, not measured: a cohort model built from a stated queen laying schedule, a development time of 21 days, a summer worker lifespan of 42 days, and a winter lifespan of 150 days produces the colony's population trajectory from a spring start of 10000 bees, reaching a peak population of 71400 on day 122. At the start of a stated main flow the brood box holds 26500 free cells, while ripened nectar at the stated flow demands 5556 cells per day, so storage binds in 4.77 days — less than a weekly inspection interval. The derived supering rule is to add a drawn super when the free cells remaining in the brood box equal 10 days of storage demand at the current flow, which is 55556 cells at the stated flow; one drawn super then absorbs 12.6 days of flow. Supering one week late at the stated flow costs 16.84 kg of honey in total: 5.57 kg that arrives after the brood box is full and is never stored, plus 11.26 kg of future gathering lost because 26500 brood cells are backfilled with nectar, suppressing laying and removing 22525 adults from the season's workforce. Two weeks late costs 34.34 kg. The practical conclusion is that supering is a decision with a deadline measured in days, and the deadline can be computed before the flow begins.