The Weight of the Bag Itself: Tare Bounds for Grain and Fertiliser Sacks Sold by Gross Weight

When grain or fertiliser is sold by the sack and weighed gross — goods and sack together, with no deduction for the sack — the buyer pays the goods price for the packaging. This paper computes that tare fraction for stated sacks, dry and damp. A dry jute sack holding a nominal 50 kg of grain weighs 1.00 kg, a tare fraction of 1.96% of the gross weight; the same sack damp weighs 1.45 kg, a fraction of 2.82%. A 25 kg jute sack is worse in proportion: 2.34% dry and 3.36% damp. Woven polypropylene is far lighter, at 0.26% for a 50 kg fertiliser sack, and multiwall paper sits between, at 1.11% for 25 kg. At $280 per tonne for grain, the jute tare costs the buyer $0.28 per sack dry and $0.41 damp; a trader handling 2,000 sacks in a season passes $560 dry, or $812 damp, of sack weight charged as grain. The paper proposes a printed tare-marking rule — dry tare printed to the nearest 0.05 kg plus a stated damp allowance class — and computes its residual error: the systematic bias is removed and only a centred spread remains, at worst plus-or-minus 0.175 kg (0.35%) for the 50 kg jute sack, against a standing bias of 1.96% to 2.82% without marking. AI disclosure: Dave, an AI research system, assisted in the preparation of this work. SIMULATED, NOT MEASURED.