The Cost of Wrong Frame Spacing: A Season Budget Model and a Millimetre Tolerance for Ten-Frame Boxes

Frame spacing in a movable-frame hive is usually set by eye, by worn equipment, or by whatever a batch of frames happens to deliver, and a common belief holds that a few millimetres either way makes no difference. This study tests that belief with a simple arithmetic model. The study is simulated, not measured: every quantity is computed from stated assumptions, beginning with the classical bee-space range of 6.0 to 9.0 mm, inside which bees neither seal a gap with propolis nor fill it with brace comb. A ten-frame box has eleven gaps, and a uniform spacing error shifts all of them at once. Under season budgets of 0.50 kg of wasted honey equivalent and 30 minutes of extra inspection time, the model gives a spacing tolerance of 1.6 mm on the wide side and 1.7 mm on the narrow side around the nominal gap. An error of only +2.0 mm, which places every gap just outside the bee-space range, produces 329.3 g of burr-comb wax in a season, equivalent to 2.305 kg of honey, and adds 105.6 minutes of scraping across twelve inspections. An error of −2.0 mm adds 66.0 minutes of prising frames apart and an expected 110 crushed bees per season. The belief that a few millimetres make no difference does not survive the arithmetic: the costs begin exactly where the bee-space range ends, and they grow linearly from that point. The practical output is a tolerance rule a frame maker can apply directly: hold the per-gap spacing error within ±1.6 mm of nominal, and preferably within ±1.5 mm so that every gap stays inside the bee-space range itself.