This is the basic format. Tap one end, water runs along the flat-bottomed gutter, drains out of the other end. Rinse, repeat. I would imagine you could get four levels high without too much water ending up in the bottom one if you had the height. Bottom one drains back into the tank. Please ignore the state of the paint It ends up shaded by plants so there is no need for mylar or anything to aid reflection.
Close up of the tap bit. Note relatively low flow.
Pump halfway up the side to increase pressure and flow at the top. Washing up sponges muffle vibration in the wall.
Fan hung centrally at the top, lights in cool tubes hanging in middle extracted from the bottom. In a 6ftx6ft room, 8.5ft high I have 3 x 600W HPS.
Wiring kept well away from water, goes out of the room through the ventilation ducting hole.
Water is not very deep initially, ends up nearly to the top of the guttering at end of flowering as roots slow the flow and grow deeper. Top of water always only just over the roots. Last cycle I got 1.104GPW and you might be able to see that I do not have room for the fourth section at the top because of a ventilation box inclusion meaning I have 11 lengths, not 12, also one whole side is half-length because there is a door there. I estimate I could get roughly 1.3 GPW in 11-12 weeks from this system (14 days veg) if I could put full-size lengths on the door side, and use the wasted space that is boxed in. I put two plants per length (one on the short lengths) for a total of 19 plants.
I have developed this over the last ten years to be very automated. The only thing I have to do manually is to fill the nutrient buckets and prime the pumps although I think this year I will automate the pump priming.
No need for any medium, I use the corrugated plastic tank top stuff cut into lengths to cover the gutter held on with cable ties. To hold the plant until it gets big enough, I use the neoprene discs from an aero propagator then throw them away at the end. Ventilation is key, there are a lot of plants in a small space so the air needs changing quite a bit. Both for humidity and temperature.
One last thing, I hang fencing about 1ft inside the guttering in a square so when the plants grow inward to the light they naturally find support there. This does mean it is a fill and forget system, it is very very difficult to get to the plants and in the last half of flowering, impossible to do so.