And, is there a point where you might not have enough fish waste to make the bog(s) prosper?
Short answer...
Yes!
Ultimately, all guidelines are more of a recommendation rather than a rule of law and this must be kept in mind. Any attempt to take guidelines to actually mean something beyond this is actually asking to entirely redefine the term.
The unfortunate angle that is not taken into consideration by surface area recommendations is the pond's depth. So, I do not view surface area recommendations with much validity.
My recommendation would be for you to use as much space as you want to use, and, with these bog filters, the more the better.
If you need specifics, then I would say 1 cubic foot of half inch Pea Gravel, with good plant growth and potentially algae growing in it, is good for 2~5x 10 inch goldfish. However, this is just an "educated" guess.
I would also be sure you have very good water flow through it and a simple foam sock pre-filter to it so to remove any large debris so that the large debris does not clog the bog faster. When the gravel becomes clogged and there is continual plant decay, then there can actually be more ammonia created rather than removing the ammonia.
Long answer...
To an extent of any
anecdotal "testing" done, it is shown in the aquaponic hobby. Bog filters, also called gravel media grow beds in aquaponics, is used quite often for backyard enthusiasts since gravel, then followed by lava rock, is incredibly cheap grow bed medium.
For biological nitrification filtering, these hobbyists go by the term "specific surface area" (SSA). SSA is the measurement of the number of square feet per cubic foot of material; in other words, this is measuring the amount of square footage surface area there is of a type of medium within a volume. Once the SSA is determined, then multiply this by the volume of the grow bed so to calculate the biological surface area (BSA). This is all determined by the size of medium in the grow bed.
If the medium is a mixture, then all linear math is thrown out of the window due too the unknown variables; in other words, then it takes an "educated" guess. Also, uncontrolled introduction of debris due to weather and plant decay also makes any suggestions incredible tough. So, the best anyone can do for you is to give you an "educated" guess, such as sometimes described by recommendations of "30% of the pond surface area".
For more info, then checkout
Bright Agrotech's (an aquaponic business) video about SSA and BSA, and, for anyone interested, here's a thread about aquaponics (
is auqaponics viable?):
Void space ratio is the amount of empty air between particles. The lower ratio indicates more potential of "fouling"; in other words, the filter will be clogged if there are no worms and other critters to dislodge the mulm so to be moved out by water flow. However, eventually, mulm is created even by worms and this mulm will clog the grow bed and this is more likely to happen if the water flow is too slow. Mulm is essentially extremely tiny bits of rock and mineral that can no longer be decomposed nor digested by any microorganisms; in other words, mulm is essentially "soil".
Bare minimum you would need around 2.5 sq. ft. of BSA per 1 gallon of water at quite low fish stocking densities and very low feeding rates. So, if your pond has 1 pound of fish per 10 gallons, then this means you need at very least 25 sq. ft. of BSA. Most common for
backyard gravel media grow beds use this rate.
Recommended level is 10 sq. ft. per 1 gallon of water or about 100 sq. ft per 1 pound of fish. This is a quite hefty amount of material and this is where wet/dry filters come into play so to improve conversion rates thus allowing less material to be used.
No matter how folk try to change the argument, the microorganism's growth will only expand according to the amount of area they are allowed to grown on. There are biological environments that will give them better conversion rates, but this is
not the same as saying the SSA or BSA is irrelevant.
Thus, using
conventional backyard gravel media grow bed recommendation and assuming you are using 0.57 inch Pea Gravel, which has 85 SSA, then this tells us 1 cu. ft. of Pea Gravel provides for 3.4 pounds of fish. This does not include the plant's and various algaes directly consuming the ammonia. So, when plants and algae is present, then 1 cu. ft. of Pea Gravel could provide for 3 times this amount.
While using
CNYKOI koi weight calculator, a 10 inch koi is around 0.5 pounds. At these small sizes, from the little research I've done, goldfish's odd body shape actually weight more than koi per inch except koi grow twice as big, in inches, than goldfish. So, this is something to take into consideration. So, if a 10 inch goldfish weighted 2 pounds, then it would take only 0.58 cu. ft of Pea Gravel per 10 inch goldfish. Remember, this does not take into account of plants and algae. So, 0.58 cu. ft of Pea Gravel could potentially manage the ammonia from 3x 10 inch goldfish.