Calculating machines required to completely fill a belt factoring in Productivity Modules and Beacons with Speed Modules

[octeris]

Hello, I hope you are all doing well.

I am trying to calculate the number of machines (in this case Electric Furnaces) required to completely fill a blue belt (45 items/sec) taking into account usage of Productivity Modules and Beacons with Speed Modules.

I was trying to follow the math shown in this Reddit thread: https://www.reddit.com/r/factorio/comme ... ing_speed/. I do not doubt the results but I want to understand the calculations involved so that I can perform the same work for any machine and crafting recipe.

I must admit my math skills are not what they used to be so I might be missing something obvious. Here's what I've got so far.

Assumptions:

• Usage of tier 3 modules in all cases
• Productivity Modules in the Electric Furnace
• Speed Modules in the Beacons

An Electric Furnace has a crafting speed multiplier of 2 therefore the speed of the machine when affected by Beacons with tier 3 Speed Modules can be represented as follows:

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s = 2 * (1 - 3/10 + b/2)
s = 7/5 + b

The items per second the machine will produce with a crafting time of c can be represented as:

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i = 1 / (c / s)
i = 1 / (c / (7/5 + b))
# I am calculating for copper smelting so c = 3.2.
i = 1 / (3.2 / (7/5 + b))

Here's where my calculation seems to break down and deviates from the results in the Reddit thread. For different beacon counts the number of copper plates per second is as follows:

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b =  0, i = 0.4375 plates per second, ~103 furnaces to fill a blue belt (rounding up)
b =  2, i = 1.0625 plates per second,  ~42 furnaces to fill a blue belt
b =  4, i = 1.6875 plates per second,  ~27 furnaces to fill a blue belt
b =  6, i = 2.3125 plates per second,  ~20 furnaces to fill a blue belt
b =  8, i = 2.9375 plates per second,  ~16 furnaces to fill a blue belt
b = 10, i = 3.5625 plates per second,  ~13 furnaces to fill a blue belt
b = 12, i = 4.1875 plates per second,  ~11 furnaces to fill a blue belt

My calculations are close to but do not match the Reddit thread. What am I missing here?

Thank you. I appreciate any help I can get on this.

[DaveMcW]

Four years ago when that thread was made, c was equal to 3.5.

[octeris]

Four years ago when that thread was made, c was equal to 3.5.

Interesting. I tried using the wiki to research recipe changes since that post was made but did not see change notes for the Copper Plate duration change. Thanks for pointing that out.

While that certainly does account for some difference, if I plug c = 3.5 into my formula they still don't line up with what was posted back then. I guess I just won't worry about it since my methodology seems correct.

[DaveMcW]

Are you adding the +20% productivity bonus?

[octeris]

Are you adding the +20% productivity bonus?

Oops. I completely forgot to account for that. That is the difference. When using c = 3.5 and the updated formula for items per second I reproduce the results of the Reddit post.

Items per second is:

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i = 1.2 / (c / (7/5 + b))
i = 1.2 / (3.2 / (7/5 + b))

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b =  0, i = 0.525 plates per second, ~86 furnaces to fill a blue belt (rounding up)
b =  2, i = 1.275 plates per second, ~36 furnaces to fill a blue belt
b =  4, i = 2.025 plates per second, ~23 furnaces to fill a blue belt
b =  6, i = 2.775 plates per second, ~17 furnaces to fill a blue belt
b =  8, i = 3.525 plates per second, ~13 furnaces to fill a blue belt
b = 10, i = 4.275 plates per second, ~11 furnaces to fill a blue belt
b = 12, i = 5.025 plates per second,  ~9 furnaces to fill a blue belt

Thanks so much for your help!

[Koub]

Once you know how to do, you may want to use this : https://kirkmcdonald.github.io/
It's extremely convenient for this kind of needs (but if you play modded, you're screwed ^^).

[mrvn]

I just put in the recipe in hellmod in-game, set the building, beacons and modules and then you can set either input or output to 1x belt type and it shows you the number of buildings needed.

Makes it easy to play with different module types or beacon numbers to get nicer ratios between buildings too.

[wobbycarly]

Rate Calculator and/or Max Rate Calculator are useful mods to have in-game for these calcs.