The expert said that, lacking calculus and a firm theory of bouyancy, it was customary with new designs that one take a ship out on a trial run, and then bring her back and modify her. For example, if a ship was topheavy, one could "girdle" her by nailing on more planks--increasing the "belly" without increasing weight that much. Or shortening masts, or even, in extreme cases, removing the upper deck.
The Vasa was just an extreme case, only lasting an hour before sinking.
You do have an option that doesn't involve calculus, though it's quite hard--make a scale model. Planing down strips to the right thickness to model planks and making sure you have taken all the other weights (cannons, sailors, etc.) into account would be a long and finicky job, but if you're trying a brand-new design it might save a lot of modification effort. I'm not sure how you'd mock up wind, but maybe just pushing would work.
If the design didn't work, you could scavenge it for part or gussy it up and use it for advertising or sell it.
I wonder if ship designers did make such test models. Search engines get swamped by modern models:
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I once had the good fortune to be touring an opera hall just as the set-builders were completing a building on one of the massive 'wagons' (floor platforms that allow quick changes of set). We'd passed through a green-room where we had already seen a model of this set piece along with a model of the whole stage structure proscenium.
All of the stagehands and set-builders were called to help push this wagon into the wing, and about halfway into the wing the top part of the set collided with a support beam of the real-building's roof.
I snuck back to the green room, saw that the stage model had this beam, and when I attempted to push the model wagon into the wing, it collided in the same place!
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