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In the end zero, because Pure Ingots.
Efficiency is one of the main concerns with automation games you will need to use math to figure out figure out ratios when manufacturing to maximize output. keep in mind belt speeds.
output of miner per minute divided by input per minute required of smelter is the number of smelters.
pure ingots is alternative recipes that uses refinery instead of smelter, these have better ratio of ore to ingot, (smelter is 1:1, refinery is 7:13) at the cost of power and needing water.
A fully loaded refinery station with piping, power etc. can take a full day to set up, while a smelting nest can be set up in an hour or so.
Tell that to FICSIT!
I enjoy the challenge(?) of maximizing a node before tapping another, so it works for me.
Pure...
120/min = 4 smelters at 100%
Upgrade to MK2 miner = 8 smelters at 100%
Upgrade to MK3 miner = 16 smelters at 100%
You can also overclock the miner at any time. You can overclocking smelters, but you are better off simply making more.
So... Make a BUNCH and then underclock them to just enough to handle your miner. Set the smelter rate to Miner-output / # of Smelters.
Note: For the sake of fun you can simply leave space for more then add them as you grow, so you don't front-load all the work.
I avoid refineries the way most people avoid the plague.
For the OP, however, you will soon find that you will need to use a lot more smelters. Instead of using one splitter to feed three smelters, trying creating a long line of smelters. On the input end of each smelter put a splitter with the input facing your miner, all in a long line. Then feed the belt from your miner into the first splitter and connect them all up. Do something similar with the smelter outputs - Put a merger at the output end of each smelter with the OUTPUT of each merger facing the same way. Hook them all up and get a bunch of ingots out of the last merger. This kind of thing takes a while to get going - The first few smelters will absorb a lot of the ores while they fill up their input buffers, but eventually everything will fill up and balance out.
The most efficient way is to use the manifold system and then max out what the belt/miner can give you.
F.ex.
120 gives you 4 smelters.
270 gives you 9 smelters.
300 gives you 10 smelters.
360 gives you 12 smelters.
et cet.
https://satisfactory.fandom.com/wiki/Manifold
https://satisfactory.fandom.com/wiki/File:Manifold_Schematics.png
Do note that by using this method and you follow the math correctly, just have patient and the last lines will fill up as time goes by. If you're left with more than it goes up in 30 (per smelter) then add one more and underclock it.
Also, overclocking the miner can give you more out of each node.