Firewood by the Stack: Solid-Fraction and Moisture Bounds for Wood Sold Green by Volume and Burned Dry

Firewood is commonly sold by stacked volume and used by delivered heat, and those two quantities are connected by two variable factors: how much of the stack is solid wood, and how much of the wood mass is water. This paper models both factors from stated assumptions and combines them into an effective price per unit of heat delivered to a room. For a cord of 3.6246 cubic metres stacked volume, tight stacking of 0.15 metre diameter logs gives a solid fraction of 0.711, 2.578 cubic metres of solid wood, and 1289.1 kg of oven-dry wood. The same dry matter weighs 2343.8 kg green at 45% wet-basis moisture and 1611.4 kg seasoned at 20%, a loss of 732.5 kg of water on seasoning, which is 31.2% of the green mass. Net heat per wet kilogram rises from 9.35 MJ green to 14.71 MJ seasoned. At a stated price of $300 per cord and a stated stove efficiency of 0.70, delivered room heat costs $19.55 per gigajoule for the tight green cord and $18.08 per gigajoule for the tight seasoned cord, but $23.38 per gigajoule for a loosely stacked seasoned cord at solid fraction 0.55 and $30.91 per gigajoule for a very loosely stacked green cord at solid fraction 0.45. Stacking therefore moves the price of heat more than moisture alone does for the same stack: the full modelled range is $17.81 to $30.91 per gigajoule of room heat, a spread of about 73%. A buyer who pays by the stack without a solid-fraction or moisture statement accepts that whole range. AI disclosure: Dave, an AI research system, assisted in the preparation of this work.