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'.
Lieste
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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.
So. Within the harbour scenario. Came off the anchorage to face south, under topsails jib and spanker. Tacked to the north gaining 4 lengths to windward, pivoting under sternway in under a ship length and gaining a course to the north with a net gain of roughly one length to windward. (Speed around 4 kts on entry). Wind on the beam.
When at 4 kts to the north, again tacked this time under reefed topsail, lost way after the turn backed the fore topsail, but continued after reversing rudder getting around to the south within around 1.5 lengths - lost more room 'gathering' under stronger leeway, but the net loss around one length, and the recovery to the beam wind had the ship pointed to the upwind side harbour exit.
I'd describe this as comfortable tacking under light sail in "Fresh Breeze (Royals etc), though not nearly as sharp as under more sail and with more way on.
Trim on a beam wind or higher can be performed with reef on the mizzen and by trimming, easing and hauling the spanker and jib, with the rudder able to be kept neutral or a point or two to favour gathering way, or staying up on the wind. This gives a minimal leeway and less trim drag when accelerating.
I carried through a tack without making sternway or performing any adjustment to the sails set (headsails eased, spanker hauled in on the approach to the wind, then reversed after backing the main and mizzen and passing through the wind). I could have carried even more speed through the tack with a moderation in canvas in places where it opposes the motion and causes merely drag.
I'll have to try from a lower speed as well, this was from a fairly high speed initiation.
The default sail trim looks a bit off - with topsail and topgallant and on a beam wind, I need to have all three headsails and rudder 'off the wind' - The mizzen needs to be shivered or furled to give even vaguely neutral trim with only 1-2 headsails.
If I set the Griping to 3 or so then I get a more controllable trim which allows all the square sails to draw, and the rudder to be trimming the course, rather than fighting the sails, small variations around here give a slight tendency to bear off the wind or come to it, but the default value (6) is too extreme IMO.
One thing which would help with coming into the wind and tacking would be adjusting the setting angle of the driver - this should be sheeted home, at the most windward angle possible to drive the stern around with no change of trim needed to keep the stern pushing through the eye and then being trimmed for minimal drag already once on the wind on the opposite tack - currently the sheeted home position is 'on' the centreline.
I know you refer to the Lively as the basis, but the broadly similar Leda class has a bit more information available... and she is a 1091 tun BM ship, displacing only around 1496 ton.
2000 is closer to the displacement of the much larger US superfrigates such as President/Constitution - 1576BM, 2200 tons.