I forgot to mention that the tomato on the window is a regular pot plant not an AP. But I seem to be getting what is meant by area for bacteria growth. Smooth river stones has far lesser area than a coconut husk of same size. So using a coconut husk will probably compensate the area for a lesser dept/volume of media.
SFG confirms that 6" is plenty of depth for most plants as long as you have support for top heavy plants, so you should be ok with 5"especially with the nutrient rich water from the AP system. Regarding filtration and that depth, that's another question, which I'll leave to wiser, more experienced folks.
I opt for dedicated filtration so media depth for filtration wouldn't be an issue. If you have a FT with its own filter them running the water through some small GB's should give you plenty of redundancy.
It's about laying out the garden in a square foot grid, and planting a different plant in each square, with density in each box dependent on what plant it is. Also recommends a mix of vermiculite, compost and moss add the medium, with only six inches of depth necessary.
I've tried it out and it works very well, can be set at table height, and is very easy to work with (nice vertical gardening tips too). I prefer building my soil, and not relying on the inputs that would be necessary, but I use the grid for most of my plantings. Saves seeds, keeps the garden neat, and allows for intensive planting.
And also why prescribe smooth stones. Surely there is a reason for that I wanna know so I may be able to weight the pros and cons.
Those who practice Aquaculture commonly say that the amount of bio-filter surface area that support the autotrophic bacteria needed to convert ammonia to nitrates is around 25 to 35 square feet per pound of fish. This assumes that there is little or no solid fish waste reaching the bio-filter.
Somewhat porous material, like expanded clay, can have increased surface area from that of a smooth sphere but the solid fish waste particles quickly fill those voids and reduce the overall surface area and advantage of the clay.
The surface area of 8-16 mm clay balls is about 79 square feet per cubic foot. This is based on a 12 mm mean diameter of the balls. This works out to be about 3 gallons of wetted bio-filter area for every pound of fish, minimum. Again, this assumes very clean water. When you add in solid fish waste, you should at least double the bio-filter size to a minimum of 6 gallons per pound of fish.
The surface area for a given volume of balls is inversely proportional to their diameter. So, if the balls were only 6 mm in diameter instead of 12 mm then they would have twice the surface area for the same overall volume, giving them about 158 square feet of surface area per cubic foot. Kaldnes, for example, has about 240 square feet of surface area per cubic foot of volume, or about three times that of 12 mm expanded clay balls; but it is not in the shape of a ball.
At one point, a few years ago, Rudolph Sittig of Easy Green/ Oekotau, the maker of Hydroton, sent us some sample bags of a new product they were thinking about marketing for Aquaponics. It was basically Hydroton 4-16. We tried it in our grow beds and it is still in there today. The small balls kept getting into our siphons and causing problems. I wish we had never received that gift.
At some point the small ball size in a grow bed becomes problematic and difficult to keep out of the siphon and plumbing. Increasing the size of the balls reduces the surface area proportionally. In the case of gravel, it is usually larger in diameter than expanded clay and gives less surface area for the autotrophic bacteria to reside. As a result, you will need more volume of media to give the same bio-filtration as the smaller diameter balls.
As to the smooth stone question, smooth stones are much easier on the hands than rough ones. This is especially important when planting and cleaning of the grow beds. The porosity of rougher stones often is offset by those nooks and crannies filling with solid fish waste and preventing the autotrophic bacteria from taking advantage of the increased surface area it offers.