Ever wondered how long before you can start building million-ton ships?
The formula is surprisingly simple:
No of construction increments = LOG[(Target size + 5000)/(Starting size + 5000)] / LOG[1 + (SBR / (10 * no of constr. incs. per year * SEC)]
SBR = Modified Annual Shipyard Build Rate (as shown in the shipyard tasks tab)
SEC = Cost of increasing shipyard capacity by 1000 tons (military shipyard)
For commercial shipyards, just make sure to divide your starting and target size by 10, and use the 10000 ton capacity increase cost (which should be the same as the 1000 ton increase for military shipyards)
This formula assumes you are using continual capacity expansion, and it produces only an idealised estimate, because of rounding used in the program. I compared the predicted shipyard size to test samples in the game and found some minor deviations that I only noticed when using the SM SY mod tool (which shows fractional shipyard sizes), but it shouldn't have any major impact.
Interestingly the growth rate of shipyards gradually slows down as they get bigger. This is because the arithmetic term disappears into irrelevance.
According to my formula, it will take me 4 years at current tech to turn a 400K ton commercial shipyard into a 3M ton shipyard, which is faster than I expected, but slower than I had hoped. I have plans for a monster 500 module asteroid miner.
