I didn't check if my pipe and filter dimensions would be sufficient before ordering the parts, so I'm doing that now.

Warning: I'm thinking out loud and it gets a little technical.
Pipe head lossI'm aiming for an aquarium turnover of about 6 times per hour. That means a flow rate of 750 l/h through the fish loop, with 800 mm static head for the gravity return flow. I chose 18x22 mm diameter tubing for the overflow and to connect the filters. This would result in a flow rate of 0.8 m/s in the tubing; that should be enough to keep it from clogging.
At 750 l/h flow, 18 mm ID straight plastic hose has about 55 mm head loss per meter. In this system, that's about 110 mm head loss through the overflow and 55 mm head loss from the SUF to the trickling filter. Let's make that 200 mm including a few bends and possible biofilm buildup; then the tubing alone takes up 25% of the total available head.

So I think I'll make at least the overflow from 32 mm PVC pipe and fittings instead. Then the head loss to the SUF should only be about 50 mm.
Static upflow filter (SUF) head loss and capacityThe SUF has an inner diameter of about 105mm, so with a flow rate of 750 l/h the upflow velocity is about 87 m/h. I hope that's low enough to keep the media static. Above a certain velocity the filter might become a moving bed filter. I've read that industrial upflow filters run at only 1-30 m/h so my SUF might be a bit undersized or overloaded
The head loss of the media is dificult to calculate as it depends on sludge buildup. I'll use about 5 liters of plastic biocarrier (similar to Kaldnes K1).
Liao & Ødegaard (2002) found that Kaldnes K1 in an upflow filter running at 30 m/h has almost 100 mm of head loss per gram per liter accumulated sludge. Assuming the specific head loss increases linearly with flow velocity, at my flow rate the head loss would be 300 mm per gram per liter accumulated sludge. So with 5 liters of media, my SUF can only catch 5 grams of solids before head loss exceeds 300 mm. I was hoping for the filter systems to be able to handle at the very least 10 grams of feed input per day, which would correspond to roughly 5 grams of solids, so I expect about 300 mm head loss if I backwash daily. I should however keep as much reserve head as possible to prevent overflowing of the aquarium. Maybe I should control the automatic backwashing with a float switch at 300 mm head loss.
Since my SUF design still has some room at the inlet in the bottom, I might try making a small radial flow filter (RFF) "hood" to settle some more particles before flowing up through the media. This would use up some head but may slow down media clogging.
Automatic cleaning of SUFI'll have to mount the SUF much lower than I thought due to the head loss. When the main loop is done, I'll start with the automatic backwash system for the SUF. I hope I can still manage to dump the backwash by gravity into a biosand filter but there may not be enough height under the SUF left for that.
Trickling filterThere will not be much gravity head left for the trickling filter either, so I will make it a bit thinner and wider than I had initially planned. The large bioballs that I've ordered (36 mm diameter) have little spunges inside so they should have plenty of surface area for nitrification, besides, the 5 liters of media in the SUF should already be plenty for nitrification even though it's not aerated. I'm more concerned about gas exchange, but I can always add air stones.
Head distribution overviewSo the 800 mm gravity head will be roughly distributed as follows:
55 mm: head loss of aquarium overflow and tubing to SUF
300 mm: expected max. SUF head loss
190 mm: reserve for SUF
55 mm: head loss in tubing from SUF to trickling filter
200 mm: trickling filter
If I change my overflow to 32 mm PVC and if the media in the SUF stays static at this flow rate, I think everything should still work out.

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-Thomas
First system (2 m³ ebb & flow, 2007-2015)
Current system (150 liter indoor, 2016-?)