I知 working on setting up some home aquaponics and I want to talk about my process. I have a lot to learn and believe that I can find others who will benefit from the journey and still others who can lend their expertise to the questions and issues I have.
Since my tanks are already set up, I知 going to skip that step for now. Obviously, there are a lot of important pieces there, but I want to talk about what I知 working on. I知 going to begin by floating some lettuces on Styrofoam in my endler tub. This tub currently runs pretty high nitrates (NO3) as there are a LOT of fish (almost exclusively females) that I acquired while breeding tiger and black bar endlers. Endlers are pretty hardy, and they don稚 seem to mind the high NO**3 *although I知 sure it痴 not ideal. The idea is that once my lettuce seed sprout, I値l get them growing in there and everyone, plants and fish alike, will be pretty happy.
To begin, I need to know how much Styrofoam I need to float the pots. A quick Google search let me know that Styrofoam will float about 55lbs/ft3. I didn稚 dive to deep into this, but it seems that different brands of foam (Styrofoam is a brand after all) will have different buoyancy (I assume slightly different). I知 working under the assumption that these will be similar enough for my purposes. Taking this, and several other factors into consideration, I will be conservative in my calculations. If I play everything on the safe side it should go just fine. The purpose here, in addition to eating my vegetables, is to get an idea of what I should be thinking about and gain understanding for it. If, in the future, I decide that there is a benefit to having exact measurements I can use my understanding to go back an make precise calculations. So here we go:

Styrofoam can float about 55lbs/ft3.
1ft = 12in
1ft3 = 12in3
1ft3 = 1728in3
Styrofoam can float about 55lbs/1728in3.
The sheets of foam that I have I got from my BIL (thanks Matt!) and you can buy it at Home Depot. The purpose of doing these calculations, however, is that you can figure out how much and random piece of Styrofoam you have can hold. I was lucky enough to get several precut sheets, but I was ready to use any random packaging that became available. Anyhow, the sheets are 48in x 14.5in x .75in. I decided that 18in was a good length based on the tub I want to float them in and also the sections in the top of my 125-gallon aquarium that will probably be the next phase of the project. So:
18in x 14.5in x .75in = 195.75in3 which comes out to be 11.3% of 1728in3. 11.3% of 55lbs is 6.2 lbs. This turned out to be a pretty convenient number. Nonetheless, I wanted to test if doubling the Styrofoam doubled the weight it could hold. So in theory two sheets can hold 12.4lbs. Click image for larger version. 

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To test my results, I used some 3lb and 5lb dumbbells that were collecting dust and was pleased with my results. One sheet of foam easily floated 6lbs (see attached photos) but began to sink when 8lbs was placed on top. Furthermore, two sheets held 11lbs no problem! When I tried to take that to 14lbs it was a no go. Once again, these aren稚 scientifically precise tests, but they will do for my purposes.
How do I know that 6.2lbs is a good amount? Well, I filled my 2in mesh pots with rocks (the growing medium I will use for now). When full, it weighed just about 3.25oz. Once again, I知 not using the exact measurement because I can manipulate the weight by adding/removing rocks if need be. Another quick google search gave me an estimated weight of full-grown leaf lettuce as 12.5oz so, full grown, each pot should weight 15.75oz, or just under 1 lb! Four pots should easily float on my foam and give me healthy room for error. Click image for larger version. 

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Potential Issues: When removing foam rounds so I can add pots, I will reduce the amount of usable foam, reducing the weight it will hold.

Next Steps/Ideas for Growth: The next major thing I am interested in is how much nitrate (NO3-) the plants will absorb. Will it halt the rise of NO3- in the tank? Reduce it? Ideally, I will take measurements while the seeds are sprouting and get an idea of how much NO3- is rising on a weekly basis currently.