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Fish to Feed Calculations

Sometimes we want to work backward from the plant side of an integrated aquaponic system, where we have determined the amount of feed we need per day to support the plant growth. One of our members requested information on how to reverse the feed calculations, so here we go. There is quite a wide variation in the amount of fish food required per square meter of plant growth. Some say 60 to 100 grams per m2 planted at 25 plants per square meter, others 25 to 30 grams and if you have seen our calculations down as low as 15 grams per square meter. We may cover those calculations again in the near future. However, in this article let’s continue from our feeding tables and design scenario from last week and work backwards to a desired result. Once you have determined which amount of feed you want to use per square meter of plant growth and this will widely vary from climatic and cultivar variations along with stage of growth. The other “tricky” part is staged growth of your fish and varied feed rates and feed composition, especially protein content. As you can see achieving the right balance is almost impossible. In our case we want to get as close as we can without straining our brain too much. Let’s say we know we will need 10kg of fish feed per day to support the amount of plant growth in our integrated hydroponic subsystem to make it a little easier for ourselves. (some coffee may be required). A little basic math There are a few simple calculations we need to do before moving on to the designing of our staging like in the previous design series. The first is reversing our feed calculations. Normally, we would calculate the amount of feed by determining the daily feed rate as a percentage of the fish body weight per day (eg %bw/day). We would take our biomass in the system and feed it X% of that per day. So, it is simply 500kg x 2% will give us a daily feed rate of 10kg. Simple. Now we reverse that to work out how much biomass we will have if feeding, in our case 10kg per day. 10kg / 2% will give us 500kg of fish biomass. We need this number to start with. You may remember in the first part of the design webinar series this formula: To calculate the yearly production we simply reverse the above formula to look like this:   Ignore the numbers in the above images.  Let’s work it out with our little scenario: Our 10kg per day at 2% supports the feed for 500kg of biomass or standing stock. Using the above pictured formula and adding our FCR of 1.8 and feed rate of 0.02 (2%) we will calculate our yearly production.  From the yearly production we will then work out the rest of our design. Example: 500kg (biomass) X 365 days (time) X 0.02 feed (%bw/day) / 1.8 (FCR) gives us a yearly production of 2028 kg.  From there we can apply that yearly production to our farm and work through the staging and see what it looks like.   You will remember the below table from our the first part of our design series: We have added our 2028 kg per year “Net Production and worked through the production and condition formula and this is what our little farm looks like.   Let’s see how close the over all feed rate of our farm is in the following table: What is interesting to note is we have upper and lower results to our expected 10kg of feed per day.  This is because the fish growth in the system is very dynamic and always changing.  We end up in the middle of each cycle at our 10kg of feed per day (10.1) which is what we are looking for.  At times we will have a little more and other times a little less but the overall average of each cycle is 10.1kg (when you take the average of the 5 variations in feed  amount through each 5 week cycle). At the same time our plant system will have growth at different stages.  I would assume you have calculated for that variation when you calculated the amount of feed you wanted each day.  Just like the fish, your plants will always be a state of flux and will cycle minimum and maximum levels of biomass. Combining the two can be quite complex.  As I said earlier it is almost impossible.  However in our scenario we have a result that is very workable and can be adjusted in operations, keeping in mind our assumptions are huge to say the least.  The great part is the formula work in practice in a well designed system. If you made it through that, well done.  I think that is enough brain hurt for one day, enjoy the rest of yours. Paul…

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