1. Potential standing crop of papyrus paper under normal swamp conditions*
A. Size of stems: Assume stems of maximum growth 15–18 ft. tall and 6 in. diameter at base. In African swamps 2 unelongated stems, 4 juvenile elongated stems, 9 mature green stems, and 13 old, dead stems occur per square meter (Gaudet, 1976 and Terer, et al, 2012). For estimate, assume 12 useable green stems per 10 square feet = 1.2 useable green stems per square foot
B. Number of slices: One tall stem (15 ft.) trimmed (thin upper part and the umbel are discarded) into 18 in. long pieces yields 8 usable pieces. Each 18 in. long piece allows about 6 slices yielding 48 slices per stem or 57 slices per square foot
C. Number of slices needed per sheet of papyrus paper: Using modern papyrus sheets (8 in. by 12 in.) about 32 slices per sheet (or 1.5 sheets per stem)
D. Number of sheets possible from a square mile of swamp: One sheet will require 0.56 square feet of swamp production. Thus, 27,878,400 (no. of square feet in one square mile) ÷ 0.56 = 50 million sheets per square mile.
E. Area available and maximum harvest possible in ancient Egypt: Of the total area 2,500 square miles perhaps 20 percent available for papermaking = 500 square miles. Thus 500 × 50 million = 25,000 million sheets possible as a biological maximum one-time yield.*
(*Note: this calculation assumes clear cutting, a one-time event)
2. Annual Sustainable Yield, if contractor constraints are followed**
A. Number of stems harvested: In Roman times (13 B.C.) as noted by Lewis (1974), contractors in one particular papyrus swamp had to pay interest in kind of 200 armfuls per day. One armful load conservatively contained 25 stems, or 5,000 stems per day. If this interest represented, say, 20 percent of the production, then 25,000 stems per day could be expected.
B. Total area required to maintain this rate of production: Assume 200-day regeneration cycle (requires 200 days maximum to grow back, 6 months or 180 days minimum); then 25,000 stems per day requires: (20,833 square feet × 200 days) ÷ 27,878,400 = 0.15 square mile (where 27,878,400 = no. of square feet in one square mile). This is the minimum size papyrus swamp plot needed. Average plantation required space for fallow, waterways, etc., thus would probably be a much larger area, say two square miles in area.
C. Maximum total sheets produced: 5,000 stems over 200 days (assume flooding during rest of year) × 1.5 = 7.5 million sheets per year.
D. Using this rate of production under contractor constraints for all of ancient Egypt:
Total swamp available in Egypt = 2,500 square mile, of which perhaps 20 percent was available for paper production, or 500 square miles = 250 plantations (2 square miles each) × 7.5 million sheets per year = 1,875 million sheets maximum sustainable yield under contractor constraints.
(**Note: this calculation assumes sustainable growth, cutting on a rotational basis)
3. Annual sustainable reasonable yield (realizing the wishes of the cartel)
A. Number of sheets produced per year: The cartel limited the labor pool (Lewis, 1974) and the area farmed. Also considering that plantations (drymoi) varied from 20 square mile (Great Swamp1) to 0.5–1.8 square mile (Arsinoite Nome2) and that modern papyrus papermakers estimate only about 100 sheets could be produced by one worker per day; best estimates are thus much less than the maximum. They are listed in Table 1 as “Sheets/yr.”