What is the theoretical yearly food production of such a system?
I think the following is a helpful start to answering the production projection question. It really depends on what we'd grow, but someone with more farming experience than me can estimate the number of plants in such area of grow beds. It looks like anything but root vegetables has a chance at growing in an aquaponic system.
But how much space do I need? Source: http://www.aquaponicshowto.com/how-much-space/page/60/ "Well that depends on how big a system you want to build and what you make the system out of. We are always being asked how big a system do I need to feed a family of four - the answer is how much does a family of four eat! Consider, how many fish do you want and how many plants do you want to grow. A 1,000 litre (264 US Gallons) tank in your aquaponics system will support between 50 and 80 fish. That will support between 1,200 (317 US Gallons) and 1,800 litres (475 US Gallons) of grow beds taken that the grow beds are about 300 millimeter (12 inches) deep.
A system made up of 1x 1,000 litre tank and two 600 litre grow beds will need at least 18 metres square (200 square feet). That is 3 m x 6 m (10 ft x 20 ft). It would support say 50 fish and a growing area of 4 square meters (44 square feet).
A system with a 2,000 litre tank (528 US Gallons) will hold about 120 to 240 fish. It will accommodate between 2,400 litres (634 US Gallons) and 3,600 litres (950 US Gallons) of grow beds.
A system made up of 1x 2,000 litre tank and four 600 litre grow beds will need at least 32 square metres (338 square feet). That is 4 m x 8 m (13 ft x 26 ft). It will support say 120 fish and 8 square metres (88 square feet) of growing area."
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