In addition to your assumptions about the redesign of the 10-pdr. Parrott, although I'm not sure the redesign took months, probably more like days...
But, you should assume that there was a great need to outfit the many new Navy ships being launched. Those big guns didn't come from thin air.
Also, I'm sure New York Harbor, Philadelphia on the Delaware River, Baltimore Harbor, certainly D.C., perhaps as far North as Boston also got heavy preference for big guns for Harbor Defense, and casting big guns would slow the production of small guns...
Taken an Interview with Capt James Benton, Feb 1864 from Pg 68 in:
So, if you saw a slowdown in production, it's not because they weren't smelting, it's because they were using different molds, and making bigger stuff! Perhaps experimenting.
I believe they had limits on how much Iron could be smelted per day, as you would expect.
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So, I'm no foundry expert, I just know what I've read about. But what I've read has raised several questions in my mind.
My first question, because they would be melting tons of iron every day, what did they do with the extra iron leftover from casting the guns, like you have to assume they would melt down more than they needed right?
So, would the leftover metal be used to cast the Parrott shells? That would make sense right? Then they could use up everything they melted down, until it was all gone, but it would also probably mean that it would be the some of the lowest quality metal, because if you are pouring molten metal, your impurities usually float, and you pour at the bottom, so any remainder iron would have the majority of the impurities in it.
At least that's my thinking, if they pour from the top of the melting pot to fill the molds, maybe that's not the case, so I don't know.
Or maybe that was a different part of the factory with it's own furnace and iron supply...
And a Second Question, casting these rifle projectiles, like for the 10 lb. Parrott, how did they get a cavity inside them anyway? Did they pour 9 lbs. of iron in the mold, and then spin the mold at a certain RPM and let centrifugal force do the rest while it cooled?
Questions you didn't know you wanted answered, am I right?