The Woodlot Regrowth Bound: How Much Land One Household Needs to Cook Forever

A household that cooks with wood can do so indefinitely only if the wood it burns each year does not exceed the wood its land grows each year. This paper turns that simple condition into a numerical bound. Starting from a stated useful cooking demand of 7.2 megajoules per day, an air-dry fuelwood energy content of 15 megajoules per kilogram, a wood density of 650 kilograms per cubic metre, stove efficiencies of 0.12, 0.25 and 0.40, and mean annual increments of 2, 8 and 20 cubic metres per hectare per year for arid, sub-humid and humid managed woodlots, the land a single household needs ranges from 1.123 hectares in the least favourable combination to 0.034 hectares in the most favourable one, a factor of 33.33 between the two extremes. Growth rate is the strongest single term, spanning a factor of 10.0 across the three climate classes, while stove efficiency spans a factor of 3.33 across the three stoves considered. The bound is stated as a formula any reader can re-evaluate with local values, together with a worked check: a household holding 0.25 hectares of sub-humid woodlot and cooking on an improved stove grows 1,300 kilograms of wood a year against a need of 700.8 kilograms, meeting 1.86 times its requirement. All results are computed, not measured, and the study is simulated, not measured.