You can tack, but usually you can't do it just with the rudder. As you are turning towards the wind, keep the topsail braced up (and loosen the headsails). You need to be able to turn far enough into the wind for the topsail to be aback. After that the wind blowing on the topsail should, hopefully, be enough to push you around the rest of the way; you might come to a stop, or be making sternway, but you should eventually go round through the wind.
Edit: the tutorial level, getting out of harbour, is practice for this.
It does! But having the simulation right there helps you learn them.
I had two main questions to answer when making this. First, how does ship physics work anyway; second, what is an appropriate UI that feels like being an officer ordering a couple of hundred people around? I previously worked on a flight sim, where it's appropriate to move a joystick, or a mouse, and have the plane respond straight away. I think that would feel wrong here - it would make the ship feel like a toy.
A benefit of the technical language is that it helps convey the idea that the ship is a big, complicated machine, with all the parts worked by people. It's also fun to see the strange words. So I decided to lean in to technical language and verbal commands. I was starting to work with git, and thought about using a command-line UI for the game; but I went with something inspired by the menus and hotkeys of old roguelikes.
I lost some hours to it. No I wouldn't say anything's terribly off, I do remember tacking being more possibly without making sternway. The ship turns slowly but should pick up some momentum once you're hard over, backing the headsails should help it go through the wind.
The tutorial level on how to get the ship pointed in the right direction and moving out of the harbour will give you the basics.