Hi Travish
All setups are slightly different (layout, nozzle type and orientation, pressure used etc) so its hard to come up with a one size fits all.
For a 4x4 chamber that deep i`d be tempted to use 9 nozzles on a 1ft x 1ft grid, suspended 6" off the chamber floor, firing upwards. If you divide the chamber into 1ft x 1ft grid each nozzle will cover 4 root sites with some overlap.
I`m going by the nozzles i use as i know what pattern they generate and how far they throw, other nozzles would be different.
When figuring what size the pump/tank needs to be, i gear everything to handle a 1 sec on/60 second off cycle just as a design reference.
Here are the theoretical calculations for a 9 nozzle system. It doesnt take account for any mist run on or changes in nozzle output versus pressure. I`ll base it on my nozzles and pressures (64-92psi) and your 20gal accumulator.
9 nozzles in a perfect world will deliver a total of 16.875ml in one second to the root chamber in a 1x1 grid.
With a 64psi cut-in and 92psi cut-out, the 20 gal accumulator has a drawdown volume of approx 19.8L (~5.25 US Gal)
Using the 1 sec/ 60 sec cycle, it`ll take approx 20 hours for the tank to drop from 92psi to 64 psi at which point the pump kicks in to put 19.8L back in the accumulator at 92psi. With TF`s cycle time of 2 sec/6 mins the tank drawdown time increases to around 59 hours. HP aero doesn`t need much of a pump
With the 1sec/60 sec cycle you deliver 1LPH to the chamber or 6.31 us gal/day.. that`s maybe 6x the amount TF is running into each of his chambers