To my mind to look at the actual building capacity of the US shipyards during the war we need to lay out conditions. I would say the following are appropriate:
- The ships should be separated out by type. A heavy frigate is worth much more than a gunboat.
- The ships should be ships which were actually built for war during the period. Converting civilian ships as gunboats is not nothing but the results are not true warships.
- We should use a consistent measure of when a ship becomes available, for example, when a ship is commissioned and available for service in a finished state. A ship which has undergone commission but which still needs work to be done to make her sail in a straight line is not strictly speaking available yet, because she was not truly finished.
- Conversions to ironclad are substantial enough that it is often reasonable to consider them as a new ship, but not always.
- If comparing to another contemporary navy that was not on a maximum war footing, then we should not measure that other navy's ships by commission (for example if they go straight to reserve, or spend years fiddling around with the sail plan before formal commission).
With that in mind:
- Heavy warships (frigates). The USN built none during the war.
- Medium warships (sloops). The USN built fifteen during the war, with several others suspended part complete.This is a rate of about four to six per year depending if you count "% of ships built" or "number of ships completed".
- Light warships (gunboats or what the RN would call gunvessels). The USN built on the order of 60-70 during the war (this number is probably incomplete as I haven't gone through all their commission dates and haven't caught the lot).
- Ironclads. The USN built roughly two dozen during the war, mostly monitor types. The larger ironclads tended to take significantly longer and many were partly finished at the end of the war.
The picture that I get overall is that the USN was able to build light ships in fairly large numbers, especially gunboats, but struggled with/had little capacity for heavy ships and over time ran into significant bottlenecks with ironclad vessels (particularly the ability to deliver the heavy plates used by the more powerful broadside ironclads such as the New Ironsides and the Webb Frigates).