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9,950 Coal
43,527.778 Crude oil
85,285.5 Copper ore
101,535 Iron ore
Rocket cost with productivy 3 in Rocket silo and every assembly machine and furnace:
3,249 Coal
12,289 Crude oil
17,375 Copper ore
33,189 Iron ore
And the above is not even considering the 30% boost to ores in miners. So you can add a 30% reduction on top of that for adding prod mods to extractors. (except oil wells, there you want speed modules).
This is all because it compounds. For instance steel plate. You get a 20% bonus when smelting the ore into iron plate. and another 20% bonus when smelting plate into steel plate . without productivity modules you would need 500 iron ore to make 100 steel plate. With productivy modules you would need 320 iron ore to make 100 steel plate.
However its not like productivity modules are this miricle module. There are draw backs. Lower construction speed (can be offset by building more factories.). Increased polution (build better walls), increased power demand (build larger power production). Huge infrastructure required to build said modules. However all the disadvantages are one time cost.
Or on oil wells but only if RNGsus hates you and gives you very little oil to work with.
Productivity is by far the worst offender when it comes to pollution and energy consumption but has its merits by actually getting you something you can't by building bigger. It becomes more and more valuable the higher you place it in the production chain until it is basically mandatory in the rocket silo, no matter the size of your base.
Efficiency is the best go to module to slap into everything when in doubt because it has only upsides. Especially good in miners since 3 level 1 mods cut down pollution to the point of making them invisible to biters.
So basically, speed mods are exclusively for depleted oil wells and to beacon up your massive endgame factories that would just become stupid large if you didn't use them, productivity slowly creeps into all the things that can hold it except for miners maybe because that pollution just becomes ridiculous and efficiency goes into everything else.
That's not necessarily true because the speed boost and energy cost are additive instead of multiplicative. In particular, slow assemblers can benefit massively - look at this example:
1x assembler mk3 with 4x PM3 consumes 881kW and gives you a crafting speed of 0.5
One beacon with 2x SM3 boosts power consumption to 1MW and crafting speed to 1.125 (125% more throughput at the cost of 13% more power drain) , so even if the beacon (480kW) is only used by a single assembler it still uses less power than the building the equivalent 2.25 assemblers. You also save 2 mk3 modules.
Speed mod beacons combined with productivity assemblers are more efficient then.
Personally I will use speed modules if I didn't plan a production line right and one of my intermediate assemblers can't keep up with demand (an example might be that I'm not making enough gears for my transport belt layout). But that's really just bad planning on my part. It's always better to just make a second assembler instead of speeding up the old one.
speed beacons are much better than most people think. for example i speed beacon my green circuit boards that's full of four productivity modules. that's 40% free stuff and it even runs faster than usual, at least in parts. i think.
yes you can always build more factories but don't forget that these level 3 cards are really expensive to build. why double the amount of factories and therefor double the amount of prod modules when you can just speed beacon the hell out of the first one with a fraction of cards needed?
i'll try to add a few screenshots in a minute.
http://steamcommunity.com/sharedfiles/filedetails/?id=865209730
http://steamcommunity.com/sharedfiles/filedetails/?id=865209708
http://steamcommunity.com/sharedfiles/filedetails/?id=865209675
note that i don't beacon the edges of the green circuits because that'd be a waste. bad screenshot by me there.
i hope that works. still unsure about the visibility settings.
I guess this information is accurate and didn't take into consideration the initial cost of those module.
What prod module do is for 10 item your produce you get one free, but you'll need to cover the initial cost before getting "true free" item. For that you'll need to build 10x the initial cost before receiving your first true free item.
If we take that on a common denominator. Let's say coal / copper / iron cost 1$. For simplification I take out of the picture the crude oil.
So a rocket without module will cost 196 770,5 $
With prod 3 it'll cost 53 813 $
You save 142 951,5 $
Again for simplification I'll take the full cost of productivity module 3.
Productivity module cost 3270 $ ( 2000 copper + 1080 iron + 190 coal ).
You can only build 44 productivity module before it's cost you more than the gain of those module.
Also that before you get "true free" item you need to spent 32 700$ for each module that you place.
For long games on low-resource maps productivity modules are useful pretty much everywhere. You can just build more assemblers or chemical plants or furnaces or whatever to get your throughput back and sticking Productivity 3 modules everywhere will almost make you forget how pitifully small and distant your resource fields actually are because productivity modules scale exponetially as the production chain gets longer.
You are right, placing 3 in the rocket silo will save you around 18% raw materials. Again you must keep the number of productivity module low. As the more you build them less materials you'll save.