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Manifolds work by splitting the available resources in half (or thirds, if you're using all sides of the splitter) over and over as the resources travel down a single line. This will eventually fill the first machine in the row, which then leaves the remaining resources to fill the next machine, and the next, and so on. Once a machine has been filled, it can then reliably draw at its normal rate of consumption. This process repeats the entire way down the line until, assuming you did the math right, all machines are running at max efficiency.
As a simple example:
You're producing 120 iron ore/min from a miner.
A smelter smelts iron ore at a rate of 30 ore/min. This means you need 4 smelters.
You place a row of 4 smelters. In front of each one is a splitter.
As the ore hits the first splitter, the resources are split; 60 ore/min to the smelter, 60 ore/min to the rest of the line.
The second smelter gets 30 ore/min from its spltter. The 3rd gets 15/min. The 4th gets 7.5/min.
As time goes by, the first smelter, being supplied with too much ore, fills up, and can now only obtain ore as quickly as it goes through it, meaning the original 60 ore/min it was getting now drops back down to the 30 ore/min that it can handle.
This process repeats to the second smelter, and the third, and finally the fourth smelter receives what remains, which is the precise 30 ore/min that it needs to function at full efficiency.
This method allows you to quickly set up simple, compact, flexible, expandable resource distribution in almost any situation. This can then be used in a similar fashion with mergers, as you then merge all of those ingots back onto a single belt to be moved to the next step in the process.
The farthest machine from the source will always run low, while the ones closest will always back up, unless you place the machines equidistant from each splitter output, each one facing directly outward from the splitter's outputs (not in a row, but in a cross pattern).
Example #1: Even Distribution. 720 splits 3 ways is 240 each. Then split this 3 ways is 80 each. Then split 2 ways is 40 each. This requires 18 smelters, overclocked to make 40/minute, for a total of 720/min.
Example #2: Dual Manifold. (For comparison sake, smelters are overclocked to 40)
1. 80 smelted. 640 passed down. Smelters 100%+ efficient.
2. 80 smelted. 560 passed down. Smelters 100%+ efficient.
3. 80 smelted. 480 passed down. Smelters 100%+ efficient.
4. 80 smelted. 400 passed down. Smelters 100%+ efficient.
5. 80 smelted. 320 passed down. Smelters 100%+ efficient.
6. 80 smelted. 240 passed down. Smelters 100%+ efficient.
7. 80 smelted. 160 passed down. Smelters 100%+ efficient.
8. 80 smelted. 80 passed down. Smelters 100%+ efficient.
9. 80 smelted. 0 passed down. Smelters exactly 100% efficient.
Dual Manifold also requires 18 smelters, overclocked to make 40/minute, for a total of 720/min.
Remember that the larger your manifold and the slower your initial PPM, the longer it takes to reach saturation and begin running at 100%
Bulk items like ores and ingots take just a few minutes to reach saturation, but slower items may take hours. In those cases, I highly recommend hand-feeding the machines' inputs as you go along programming them.
Similarly, I also recommend feeding the manifold and powering the machines as you build them versus waiting until it's all done. That way, construction and saturation coincide.
Finally, building the entire "trunk" of the manifold with the highest belt speed (same as the input) and using the slowest possible belt for each takeoff also speeds up saturation time.
If you use parallel splitting solutions then you have to modify the splitter design depending upon how exactly how many machines you are going to use and the exact split that each machine needs. If you extend the line to add more input then you have to redesign the splitting solution. In a serial splitting solution you just assume that the input hoppers of everything will be saturated and in that case they will just take as much they can use and as long as you didn't put in more consumers than you can provide resources everything will be produced at its maximum rate. In practice you have to wait a few minutes for the input hoppers of such a factory to fill up before it will have the ideal split. Until then the factory will produce unbalanced outputs. This is the price you pay for the simplicity of the design and layout requirement.
You can decide whether you want to make a custom parallel splitting solution for each factory that is more difficult to duplicate and expand later or you want to easily expand your factory by using a splitting method with no thought required, but you have to have a bit of wasted materials sitting around in hoppers before the machines run the way you are intending.
When I first started (am still on my first game) all I had were Mk1 belts, so it was obligatory load balancing for most things.
If you like running belts along the wall and hooking them with Splitters you're already using a manifold, but you can load-balance from there. If nothing else is hooking that belt it's not really a "manifold" yet anyway, just some extra belt.
If uranium fuel rods are radioactive that's an even better reason not to line the walls with them ...
Since it depends on multiple trains for supplies, I'm not going to activate it until after signalling lands so my nuclear fuel trains don't crash and stall my fuel production