Loaf of Bread

How much wheat could you produce each year, using the fertilizer from one adult’s urine?

We start with the amount of nitrogen, phosphorus, and potassium in one adult’s annual urine output(1):

Nitrogen (N): 4,000 g  (8.81 lbs)

Phosphorus (P): 365 g  (0.8 lbs)

Potassium (K): 1,000 g  (2.2 lbs)

Nitrogen:

Nitrogen must be added every year, because it is the nutrient plants use the most of, and it is not persistent in the soil. From USDA statistics on fertilizer use and production in wheat across the entire United States over  5-year period (2, 3), we can see how much wheat was grown on average with a given amount  of nitrogen fertilizer:

Total nitrogen fertilizer applied and wheat harvest yield (U.S.)
Year N applied (thousands of short tons) Wheat harvest (thousands of bushels) Bushels wheat/ton N Lbs wheat/lb N
2007 1689 2051088 1214 36.4
2008 1647 2499161 1517 45.5
2009 1394 2218061 1591 47.7
2010 1331 2209916 1660 49.8
2011 1692 2244557 1496 44.9
Average 1692 2244557 1496 43.7

 

The figure in the bottom right cell of the table above is the ratio of how many pounds of wheat can be grown with a pound of nitrogen. Though calculated using pounds, the ratio is unitless and can be used with grams, kilograms, or any mass unit. Thus:

8.81 lbs of N (one adult’s annual urine contribution) can produce 8.81 x 43.7 = 385 pounds of wheat.

4.0 kg of N (same as 8.81 lbs) can produce 4.0 x 43.7 = 174.8 kg of wheat.

The nitrogen (N) is sufficient to grow 174.8 kg (385 lbs) of wheat.

Potassium and phosphorus:

Potassium (K) and phosphorus (P) are also essential to plant growth, but they are required in smaller volume than nitrogen. They are also persistent in soil, so while a deficient soil will need heavy application of P and K, a soil with an adequate amount of these nutrients will only need as much P and K applied as fertilizer to replace that which is removed in the harvested crop.

According to the Cornell University Cooperative Extension(4), bone-dry wheat contains 0.66% P2O5 equivalent. Translating to elemental P values (because P2O5 contains only 44% P), dry wheat contains only 0.29% P. Since harvested wheat has about 87% dry matter content, it contains 0.25% P by weight. Therefore, one unit of P can produce 1 / 0.25% = 400 units of wheat.

From our urine production values at the beginning, we have 0.365 kg P, which can produce 0.365 x 400 = 146 kg of wheat = 322 lbs.

The Phosphorus (P) is sufficient to grow 146 kg (322 lbs) of wheat.

Wheat contains 0.31 lbs K2O/bushel(5) = 0.31 lbs K2O/60 lbs  wheat. Thus wheat contains 0.51% K2O = 0.43% K. One unit of K can produce 1 / 0.43% = 233 units of wheat.

Therefore, the 1 kg of K in an adult’s annual urine output can produce 1 x 233 = 233 kg wheat = 513 lbs.

The potassium (K) is sufficient to grow 233 kg (513 lbs) of wheat.

What does it add up to?

To figure out how much wheat can be grown using an adult’s annual urine production, we need to figure out which nutrient is the most limiting, or in shortest supply. Looking back at the total projected yield based on each of the three macronutrients (NPK), it is apparent that phosphorus (P) is the most limiting, as it is only sufficient to produce 146 kg (322 lbs) of wheat.

So our answer is that the urine produced by one adult during a year contains the fertilizer needed grow 146 kg, or 322 lbs of wheat.

How much bread can 400 g of wheat make? Two of the most popular bread recipes on the King Arthur Flour website (6, 7) average 397 g/loaf, so:

The urine produced by an adult in one day contains enough fertilizer to grow all the wheat in one loaf of bread.

References:

  1. Nitrogen, Phosphorus, and Potassium per capita annual production taken from Vinnerås, Bjorn. 2002. Possibilities for sustainable nutrient recycling by faecal separation combined with urine diversion. Agraria 353, Acta Universitatis Agriculturae Sueciae, Swedish University of Agricultural Sciences. Uppsala, Sweden.
  2. http://www.nass.usda.gov/Publications/Ag_Statistics/2011/Chapter01.pdf (yields)
  3. http://www.ers.usda.gov/data-products/fertilizer-use-and-price.aspx#26720 (fertilizer use)
  4. http://nmsp.cals.cornell.edu/publications/factsheets/factsheet28.pdf
  5. http://www.cropnutrition.com/efu-potassium#removal-by-crops
  6. http://www.kingarthurflour.com/recipes/new-white-breakfast-bread-recipe
  7. http://www.kingarthurflour.com/recipes/hearth-bread-recipe

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