Is there an issue with backed sail producing a turning moment when making way astern which is opposite in sign to that expected.
(in the eye of the wind, with backed mizzen alone, set a full stack of sail - I'd expect drag to take the stern downwind, I'd also expect the pressure on the backed sail to drive the stern away. from the wind. Currently the stern will draw up under that condition, even with rudder set for the desired coming through the eye while making sternway). This seems to warrant investigation, as it is counter my expectation.
I'm not sure what you mean by driving the stern away from the wind. Surely when you start off in eye of the wind, then whichever way the stern turns, port or starboard, it's into the wind?
This is the behaviour I see now. If I start off in the eye of the wind, and set just the mizzen topsail and topgallant, braced up on the port side, then as expected this pushes the stern over to port (so the head of the ship turns to starboard). However if, after the ship has gathered some sternway, I then brace the mizzen sails up on the starboard side, the stern continues going slowly to port, rather than coming around the other way.
What's happening in this second part is that there are two forces fighting against each other. The hull going backwards has some angle of attack on it, so the lift force is generating torque making it want the stern want to turn even further to port; while the sail is trying to push it the other way. I think the hydrodynamic torque is way too strong now, because the lift force is acting too far aft. Essentially it's the same issue as the "griping" control, but when going backwards. Effectively the backwards griping is set at 20. A quick test shows the sails having more effect if I set this to 10, but I'm not sure what the correct behaviour is.
A bare hull should turn to port when driving forward with the rudder set to turn to port. It should also drive to port when the rudder is sent over (and we seem to miss an explicit command to reset the rudder midships) to turn to starboard but with sternway on. This should be at roughly the same radius regardless of speed in the absence of strong trim from the rig.
When you set sail balance ahead of the centre of lateral effort the head should fall off the wind, with the balance behind the lateral effort the head should come to.
"Eye of the wind" is listed over a range from roughly the bracing angle of the yard through the wind in your reporting. This is the usage I made - and with the rudder and mizzen stack and spanker all working together to bring the head around I cannot see the head falling off being a reasonable outcome.
The scale of drag from backed sails seems much lower than the drawing of a driving sail, but this is contradictory to my understanding, where the CD max of a cloth airfoil at 90 degrees is closer to 2.0, with the 'filling and lifting' portion of the drag and lift curve being only important at the relatively low angles of attack. CD being relatively flat function of AOA over the 'draggy' portion of 'non lift'.
So when I teleport-turn the ship into the position below, the bow falls off the wind. I believe this is the scenario Lieste is describing as counterintuitive. However, if I repeat the experiment with all fore-and-after canvas doused, the ship turns bow to wind and even tacks itself. So the aerodynamic behavior of the square sails seems to be correct. This raises the interesting question of whether it is possible to tack the frigate while stationary...