Right now I'm trying to figure out the logistics and have the sketchup perfected before I build the system.
Kudos. A lot of people jump in with both feet without testing the water depths first!
Physics I'm in need of help with, what are the formulas to efficiently calculate what the level should be for each phase to utilize gravity and feed the system with only a pump initially feeding water with X head.
The water volumes and levels etc are dependent on the media you intend to use in your GB. If your two "half" IBC GBs are actually only 400L of media which holds say 120 - 220L of water each, then you'll be drawing up to 440L of water from the FTs.
Although a lot of people say their IBC FT is 1000L most often its only got about 800-900L of water actually in it, so taking out up to half of the water might be a bit extreme for the fish. This is where the sump comes in handy. If your sump contains as much water as the GBs will require to flood to their appropriate level (plus a bit more for system losses, evaporation and transpiration between top ups) then you can have a CHIFT PIST (CHOP) system.
In your case though, with two 1000L IBC FTs, you can easily get by without a sump, with the water level dropping from 900L to 680L (less however much is in the pipework) at the peak of the GB flood (assumes a perfect flow between the two FTs which are perfectly level). This alleviates the need for the extra troughs and makes plumbing a lot more simple. "Simplicity is a key to success."
File comment: 2 x IBC FT, 2 x 1/2 IBC GB, one pump
2ibc.jpg [ 17.98 KiB | Viewed 1914 times ]
2 X 1000L IBC FT (filled to 900L, 100L ullage, each) = 1800L
You have 1800L of water which needs to pass through the filtration each hour. If you want to run continuous flow then you only need a 1800lph pump (or slightly larger to account for head loss). If you want to run timed flood and drain, say 15/45, then you're going to need a pump of at least 1800 / 0.25 = 7200lph (plus, for head loss)
To compute head loss, you need to know the height from the surface of the FT from where the water will be drawn to the maximum height through which the pump is required to deliver water; this is easily measured with a tape measure in most instances. You also need to account for pipe friction and the configuration of your plumbing; 90 degree bends impose substantially more resistance to flow (and hence head loss) than does a 45 degree elbow; the further water has to flow (linear distance) the more the losses. Unless you're having to be exact, in most BYAP projects pipe losses are not that significant that they have to be precisely computed, and in most cases they are substantially smaller than the losses associated with pumping vertically against gravity. Just have a look at the capacity vs. head graphs for each pump and select the pump which best suits your design.
My overall plan, what are the fatal mistakes I'm making that only someone with so little experience would overlook?
Not understanding where all of your water is at any time, and thinking stocking density is dependent only on the volume of water in a system and ignoring the filtration capacity.
How do I approach the volume and height calculations?
Draw a picture first, personally I use pencil and paper as I am faster at using these simple tools than I am at using computer based tools.
Main concern I have is if the pumps fail and all the water drain out of the system since it's gravity fed what levels do I keep everything to prevent over flow? Are there techniques I haven't found yet?
KISS. Let gravity be your friend not your enemy. With a pump in the FT, your biggest concern should be if the plumbing fails and water is not returning to the FT, you could pump the FT dry; this is easily overcome with a float switch to switch off the pump if there is an exceptionally low tide, changing the configuration of the pump intake to force the pump to lose suction in the event of an extremely low tide, or plinthing the pump off the bottom of the tank so it loses suction at extremely low tide (or a combination!)
The next concern is if the pump fails and this is your only source of oxygenation, what are you going to do? Do you have an air pump on a different power supply? Do you have a backup pump on a different power supply?
I'm a novice so not looking to maximize stocking densities yet, I intend to build the system and grow from there to find out what densities work best for what I have. There isn't enough data in aquaponics to calculate efficiency levels from design, just approximations.
What are you trying to grow? Fish? Or plants? In my case I want the plants and veges, the fish are just an edible by-product. In this case, the stocking density is much lower and therefore has lower risk (or at least less adverse consequences in the event of realised risk events). If you're system is biased toward growing out the fish and the GBs full of veges and flowers are the by-product then you're going to push boundaries so you're going to need to be much more risk aware and have more complexity on your systems and more fail-safes. Again, KISS.
When the system is first installed and fully cycled, I'd not be adding any more than about 2kg (harvest weight) of fish in each of your systems because you only have about 800L of filtration in each. This limit seems quite severe, but later when the system is more mature and you have all the required safe-guards in place, you could push this density a LITTLE more.
You might consider redesigning the system to incorporate the troughs you mention as extra GBs and/or sumps? Or chop up another IBC to have 3 "half" IBC GBs with a full IBC FT and a "half" IBC sump? Or acquire another IBC and use this in the sump, then you could end up with something like:
File comment: IBC CHIFT PIST
ibc chift pist.jpg [ 20.57 KiB | Viewed 1914 times ]
If you've got two pumps on separate timers you could interlock them with some simple electrical relays and share the sump between your two symmetrical systems?
The options are too numerous, and I don't know any of the constraints you've got, like space, money etc. Think about the design some more and post your eventual concept and I'm sure someone will highlight any potential errors or omissions. It's easier to change a plan than it is to change the project after its built.
2008-2009: Experimental, NFT
2010-2012: IBC system(s)
2012-Now : 1000L FT, 500L GB, 23/25 trout (added 27Apr. 2 jumpers)