How would I make a setup that would fill the bottom chest first and then once that's full fill the next one up until it reaches the top? I know of the standard design for this, but I want a faster design. I know that putting two hoppers into a chest doubles the speed at which the items move into the chest. What is the fastest way to create a setup that fills like this?
Assuming a stack of chests (54 slots each) and limited to vanilla without command blocks:
In theory one could have only the end of the chest stack exposed and fill each from hoppers on the other five adjacent blocks, but this would mean filling five hoppers per chest as well…
Droppers can be clocked to push items faster than hoppers (but require the same sort of multiple hopper feeds to avoid becoming limited once the dropper itself empties).
Using this to fill a stack of chests would, however, require a separate feed line for each chest (and associated RS to switch between them). [One could also fill the chests simultaneously.]
This might be viable if the input stream was a recirculating (AFK-pool style) waterstream being fed by the output of a large farm and employing three hopper pipes per dropper, for example. [The droppers and hopper pipes would also tend to fill, but – under this sort of circumstance – that might be acceptable…]
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WARNING: I have an extemely "grindy" playstyle; YMMV — if this doesn't seem fun to you, mine what you can from it & bin the rest.