Dung Cakes Priced Twice: Heat Delivered per Kilogram and the Fertiliser Destroyed by Burning It

A kilogram of dried dung cake is priced twice in a single account: once for the heat it delivers in a stove, and once for the fertiliser that burning destroys. Fresh cattle dung is stated at 80 percent moisture on a wet basis, dried to a burnable 12 percent, with dry matter at 14.0 MJ per kilogram and a stated stove efficiency of 0.18. One kilogram of dried cake therefore requires 4.4 kg of fresh dung, loses 3.4 kg of water over 5.15 days of stated sun drying, and delivers 2.165 MJ of useful heat. The same kilogram contains 15.84 g of nitrogen, 3.52 g of phosphorus and 12.32 g of potassium; burning destroys 15.05 g of the nitrogen, while the phosphorus and potassium survive in ash if the ash is returned to the field. Valued at a stated purchased-wood price, the heat in one kilogram is worth 0.0641 US dollars, against a grain-yield loss of 0.198 kg of grain on depleted soil, 0.1188 kg on moderate soil and 0.0396 kg on fertile soil. Burning is the rational choice on these numbers whenever the grain response to available nitrogen stays below 32.4 kg of grain per kilogram of available nitrogen, which holds for all three stated soil states when the alternative fuel must be bought; it ceases to be rational when the alternative fuel costs nothing, because the heat then has no offsetting value while the nitrogen loss is unchanged. This study is simulated, not measured. SIMULATED, NOT MEASURED.