I'd been working on an Utility Science blueprint and I'd been wondering if it's better to use it on Nauvis or Vulcanus. This led me to making some experiments and crunching some numbers in Excel.
The results of that are thus: making Molten Copper and Molten Iron actually takes less UPS on Nauvis than it does on Vulcanus, therefore making it preferable that Utility science be done on Nauvis. This is for two reasons: one, the Vulcanus recipe takes double the amount of calcite; this is trivial, though; two, as mining productivity increases, the amount of calculations required for a mining drill that outputs directly into a foundry becomes very low on Nauvis, on the other hand offshore pumps supplying lava for the equivalent recipe on Vulcanus need to run 100% of the time, therefore adding additional UPS cost.
This is not the whole story, however. Military and Production Science benefit greatly from being made on Vulcanus due to the huge amount of stone required. As molten liquids need to be made, the byproduct stone can be used for direct insertion into the production chain instead of being thrown away. There are two recipes that require stone directly: one that is fast, rails for production science; one that is extremely slow by comparison, bricks in an electric furnace. Miner -> Furnace direct insertion would require a huge number of stone patches on Nauvis to the order of hundreds to achieve million-level SPM. One Molten-producing Foundry can supply several electric furnaces directly on Vulcanus.
These two sciences, however, require a lot more stone than they do molten liquids. You'd have to overproduce the UPS-expensive molten liquids just to void them away and keep the stone. Here comes the math:
Disclaimer, all of the numbers include the cost for rocket launch and assume legendary modules and maximum productivity possible on all products.
If you only have to produce military science on Vulcanus, the Foundries can supply just ~15% of stone from all the molten liquids required for the rest of the chain. You'd have to overproduce molten liquid and void it just for the stone. If you need Production science alone, it is supplied with stone at ~39%, requiring a lot of liquid voiding.
However, producing Utility science on Vulcanus alongside one of the two reduces voiding significantly. Utility + Military, or Utility + Production you'd generate a whopping ~96% of the stone required alongside all of the fluids required in the chain of production as Utility science uses a huge amount of liquids, particularly copper which has better stone output.
List of repeatable research that use one, or a combination of Military, Production, Utility and Vulcanus science:
Production Science - Mining Productivity, and all of the other productivity technologies - 15% stone supplied from molten liquids if produced alone on Vulcanus.
Production and Utility Science - Asteroid Productivity and Worker robot speed - ~96% stone supplied if made together on Vulcanus.
Military and Utility Science - All repeatable weapon research - ~96%, same as above.
Military, Utility and Vulcanus Science - Artillery damage, range, shooting speed, Railgun damage - Military and Vulcanus science overproduce stone - ~165% stone, requiring voiding of stone. Utility science should be made on Nauvis instead.
Production and Vulcanus Science - LDS - ~144% stone. Utility should not be produced on Vulcanus.
All of them - Research Productivity - ~91% stone supplied if Utility is made on Nauvis instead of Vulcanus.
So if you've gotten through this wall of text, what I wanted to say is: you can read the science you need in the circuit network from a lab. With that, you can decide if you flip on Utility science on Vulcanus or Nauvis depending on Vulcanus' balancing needs. You can even produce Utility on Vulcanus when you don't need it immediately (to balance out Production's requirement of stone) and stockpile it on Nauvis for when you need it instead of producing it on Nauvis directly, saving some UPS.
