It's a lot of micromanagement at least at the beginning (until you get to ships with decent hull strength). So, it depends on the matchup.
Example 1:
A frigate (6th or 5th rate) against a galleon (typical for an early game matchup), of course 5th rate is much better for this due to more 'bang' of its 48 cannons.
I would have to maneuver the frigate a lot in order to stay out of the 30 broadside guns of the galleon. Ironically, it seems, it is easier to do it when the frigate is ahead of the galleon in terms of wind. Something like this:
-- wind --> galleon ----> frigate
The galleon would be in hot pursuit (yet slower than the frigate) with all sails out (important for the chainshot to work well), so the frigate can do a quick turn while staying out of galleon's gun range (galleon is slower to turn too), fire a salvo of chain and turn back into the wind (to run) again. Rinse, repeat until the galleon's sails are down, bringing it to crawl. Once that's done, the frigate can make either make a big loop around the galleon and fire into it's backside or just fire from the front until the galleon surrenders. This is how I built my Dutch fleet in the early game (No shipyards, just enemy captures).
Note, that this might be way harder to pull off on higher battle difficulties (I play on normal) since the AI galleon would have sniper-like accuracy... So, one missed turn and it's good-bye frigate!...
I've pursued similar tactic with a sloop versus a flyut. It's possible, but much harder due to the lower fire-power of the sloop. I've had no problem demasting Indiamen and the like with a sloop though.
Example 2:
SOLs (any are good) versus a fleet. I'd break my fleet into a few groups (of two, three ships in each) and try to circle at the maximum range of chainshot firing the AI's vessels.
You will take damage (from AI's roundshots) this way though (so, there is the "luck" factor), but 3 chain salvos from passing SOLs (even fourth rates) against a ship with all sails out can bring it down to a crawl. The key with this tactic is not to get entangled in battle with the slowed down ships, but to sail away drawing the remaining, healthy AI's ships towards you while the ones with damaged sails remain behind. By the end of the battle I would have a messy battlfield littered with AI's ship trunks still dangerous since they have many cannons and healthy hulls. So I'd sail up to each of them and "finish off the job" from a safe angle.
If both fleets are big (many ships), this can take a long time, so you might need more than an hour for a battle (can be set in the options before entering the battlefield) if you're attacking.
Prize money
It's not uncommon to see prize money in the range of 5000 to 10,000 gold after a big sea battle with many ships captured. Not a small change in the early years of the game...
Battle speed.
Until you've really got the feel of it, I'd recommend switching the battle speed from 'normal' to 'half speed' during the crucial moments. That at least gives you time to react. Those AI ships (with any sails left) can turn darned fast (one of the very unrealistic features of ETW).
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