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Component calculations and ratios

4 months ago

10 min read

Aquaponic systems need to be balanced. The fish (and thus, fish feed) need to supply adequate nutrients for the plants; the plants need to filter the water for the fish. The biofilter needs to be large enough to process all of the fish wastes, and enough water volume is needed to circulate this system. This balance can be tricky to achieve in a new system, but this section provides helpful calculations to estimate the sizes of each of the components.

Plant growing area, amount of fish feed and amount of fish

The most successful way to balance an aquaponic system is to use the feed rate ratio described in Section 2.1.4. This ratio is the most important calculation for aquaponics so that the fish and plants can thrive symbiotically within the aquaponic ecosystem.

The ratio estimates how much fish feed should be added each day to the system, and it is calculated based on the area available for plant growth. This ratio depends on the type of plant being grown; fruiting vegetables require about one-third more nutrients than leafy greens to support flowers and fruit development. The type of feed also influences the feed rate ratio, and all calculations provided here assume an industry standard fish feed with 32 percent protein.

Leafy green plants Fruiting vegetables
40-50 g of fish feed per square metre per day 50-80 g of fish feed per square metre per day

The recommended first step in the calculation is to determine how many plants are desired. On average, plants can be grown at the planting density shown below (Figure 8.1). These figures are only averages, and many variables exist depending on plant type and harvest size, and therefore should only be used as guidelines.

Leafy green plants Fruiting vegetables
20-25 plants per square metre 4-8 plants per square metre

Once the desired number of plants has been chosen, it is then possible to determine the amount of growing area needed and, consequently, the amount of fish feed that should be added to the system every day can be determined.

Once the amounts of growing area and fish feed have been calculated, it is possible to determine the biomass of the fish needed to eat this fish feed. Different-sized fish have different feed requirements and regimes, this means that many small fish eat as much as a few large fish. In terms of balancing an aquaponic unit, the actual number of fish is not as important as the total biomass of fish in the tank. On average, for the species discussed in Section 7.4, the fish will consume 1-2 percent of their body weight per day during the grow-out stage. This assumes that the fish are larger than 50 g because small fish eat more than large ones, as a percentage of body weight.

Fish feeding rate
1-2 % of total body weight per day

The example below demonstrates how to conduct this set of calculations, determining that, in order to produce 25 heads of lettuce per week, an aquaponic system should have 10-20 kg of fish, fed 200 grams of feed per day, and have a growing area of 4 m2. The calculations are as follows:

Lettuce requires 4 weeks to grow once the seedlings are transplanted into the system, and 25 heads per week are harvested, therefore:

Each 25 heads of lettuce require 1 m2 of growing space, therefore:

Each square metre of growing space requires 50 g of fish feed per day, therefore:

The fish (biomass) in a system eats 1–2 percent of their body weight per day,

therefore:

Although extremely helpful, this feed ratio is really only a guide, particularly for small-scale units. There are many variables involved with this ratio, including the size and type of fish, water temperature, protein content of the feed and nutrient demands of the plants, which may change significantly over a growing season. These changes may require the farmer to adjust the feeding rate.

Testing the water for nitrogen helps to determine if the system remains in balance. If nitrate levels are too low (less than 5 mg/litre), then slowly increase the feed rate per day without overfeeding the fish. If the nitrate levels are stable, then there may be deficiencies in other nutrients and supplementation may be required especially for calcium, potassium and iron. If nitrate levels are increasing, then occasional water exchanges will be necessary as nitrate rises above 150 mg/litre. Increasing nitrate levels suggest that the concentration of other essential nutrients is adequate.

Water volume

The water volume is most important to the aquaculture aspect of aquaponics. Different stocking densities affect fish growth and health, and are one of the most common root causes for fish stress. However, the total water volume does not affect the hydroponic component, except that with large volumes of water it takes more time for the water to accumulate a substantial nutrient concentration during the initial cycling. Thus, if a unit has a relatively large water volume, the only impact is that it would take longer to reach the optimal nutrient concentrations for plants. Large water volumes help to mitigate changes in water quality, but may mask problems for longer. The DWC method always has a higher total water volume than the NFT or media beds.

The recommended maximum stocking density is 20 kg of fish for 1 000 litres of water (fish tank). The small-scale units described in this publication have about 1 000 litres of water and should contain 10-20 kg of fish. Higher stocking densities require more sophisticated aeration techniques to keep the DO levels stable for fish, as well as a more complex filtration system to deal with the solid waste. New aquaponic farmers are strongly recommended not to exceed the stocking density of 20 kg per 1 000 litres. This is particularly the case where a constant electricity supply is not guaranteed, because a brief interruption can kill all of the fish within an hour at high stocking densities. This same stocking density applies for any size tank larger than 500 litres; simply use this ratio to calculate the maximum stocking density for the given volume of water. If the tank is smaller than 500 litres, reduce stocking density to one-half, or 1 kg per 100 litres, though it is not recommended to grow fish for consumption in a tank smaller than 500 litres. For reference, an average tilapia weighs 500 g at harvest size and 50 g at stocking size.

Fish stocking density
10-20 kg of fish per 1 000 litres of water

Filtration requirements - biofilter and mechanical separator

The amount of biofiltration necessary in aquaponics is determined by the amount of feed entering the system daily. The main consideration is the type of biofilter material and surface area of that medium. The larger the surface area, the larger the bacterial colony that can be hosted and the faster ammonia is converted into nitrate. Two ratios are provided, one for the volcanic gravel found in media beds, and one for the Bioballs® found in NFT and DWC units. This calculation should be considered a minimum, and excess biofiltration does not harm the system but rather makes the system more resilient against ammonia and nitrite spikes. Biofilters should be oversized if it is suspected that low temperatures could affect bacterial activity. Appendix 4 contains more information on sizing biofilters and calculating the volume required.

Biofilter material Specific surface area (m²/m³) Volume required (litres/g of feed)
Volcanic gravel 300 1
Bioballs® 600 0.5

The mechanical separator should be sized based on the volume of water. Generally, the mechanical separator should have a volume of 10-30 percent of the fish tank size. Mechanical filters are needed for both the NFT and DWC systems, as well as media bed systems with high stocking densities (> 20 kg/1 000 litres).

Summary of component calculations

  • The feed rate ratio provides a way to balance the components of an aquaponic system, and to calculate planting area, fish feed, and fish biomass.

  • Feed rate ratio for aquaponics:

  • 40-50 grams of daily feed per square metre (leafy greens);

  • 50-80 grams of daily feed per square metre (fruiting vegetables).

  • Fish feeding rate: 1-2 percent of their body weight per day.

  • Fish stocking density: 10-20 kg/1 000 litres.

  • Biofiltration volume:

  • 1 litre per gram of daily feed (cinders in media beds)

  • ½ litre per gram of daily feed (Bioballs® in NFT and DWC)

Table 8.1 summarizes the key figures and ratios for designing small-scale media bed, NFT and DWC units. It is important to be aware that the figures are just guides as other external factors (e.g. climate conditions, access to a constant supply of electricity) may change the design on the ground. Please note the footnotes below the table explaining the figures and the applicability of each column per aquaponic method.

TABLE 8.1
Practical system design guide for small-scale aquaponic units

Fish tank volume (litre)Max. fish biomass1 (kg)Feed rate2 (g/day)Pump flow rate (litre/h)Filters volume3 (litre)Min. volume of biofilter media4 (litre)Plant growing area5(m²)Volcanic tuffBioballs®2005508002050251500101001 20020–501005021 000202002 000100–20020010041 500303002 500200–30030015062 000404003 200300–40040020083 000606004 500400–50060030012

Notes:

1. The recommended fish density is based on a maximum stocking density of 20 kg/1 000 litres. Higher densities are possible with further aeration and mechanical filtration, but this is not recommended for beginners.

2. The recommended feeding rate is 1 percent of body weight per day for fish of more than 100 g of body mass. The feeding rate ratio is: 40-50 g/m2 for leafy greens; and 50-80 g/m2 for fruiting vegetables.

3. The volumes for mechanical separator and biofilter should be 10-30 percent of total fish tank volume. In reality, the choice of containers depends on their size, cost and availability. Biofilters are only needed for NFT and DWC units; mechanical separators are applicable for NFT, DWC units and media bed units with a fish density of more than 20 kg/1 000 litres.

4. These figures assume the bacteria are in optimal conditions all the time. If not, for a certain period (winter), extra filtration media may need to be added as a buffer. Different values are provided for the two most common biofilter media based on their respective specific surface area.

5. Figures for plant growing space include only leafy greens. Fruiting vegetables would have a slightly lower area.

Source: Food and Agriculture Organization of the United Nations, 2014, Christopher Somerville, Moti Cohen, Edoardo Pantanella, Austin Stankus and Alessandro Lovatelli, Small-scale aquaponic food production, http://www.fao.org/3/a-i4021e.pdf. Reproduced with permission.

Food and Agriculture Organization of the United Nations

http://www.fao.org/

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