Historical data

Some quantitative historical sources:

W. Froude, "The Resistance of Ships"
https://archive.org/details/resistanceships00frougoog

This records drag experiments on a wooden ship, from 1871. The numbers give a drag coefficient of 0.0045. I tried this, but it made things too slow, going by other sources, so I have reduced it. A typical modern figure is around 0.0025.

P. Decenciere, "Three French Sailing Ship Performance Trials", Mariner's Mirror, 2008; and "Some Eighteenth- and Nineteenth-century French Trials of Square-rigged Warships Tacking", Mariner's Mirror, 2011.

"Performance Trials" has some very nice polar diagrams, including one for the Jean Bart, an old-fashioned 80-gun ship tested in the 1870s. At a wind speed of 9m/s it shows around:

8 kts close-hauled
10.5 kts on the beam
9 kts on the quarter
7.5 kts before the wind

This is without studdingsails, but presumably with royals. Studdingsails add about a knot and a half. Speeds with less wind are roughly proportionally lower.

"Warships Tacking" is gold dust, and includes timings of the different steps in the tacking procedure, and in some cases even speeds throughout so that you can chart the ship's track. Typical timings are, for a 64-gun ship starting close-hauled at 5kts,

0s- start the turn with the helm (?)
55s - foresails aback
2m - wind right ahead
3m - ship dead in the water
4m 15s - making way
4m 45s - close hauled on the new tack
(with big variations on the later steps).

A.M. Glebov, "The Analysis of Propulsive Quality, Stability and Controllability of the Ships of the Black Sea Fleet During the Russian-Turkish War of 1828–1829 Basing on Contemporary Data" (in Russian) 2012
http://izvestia.asu.ru/2012/4-2/hist/TheNewsOfASU-2012-4-2-hist-10.pdf

See MartesZ's post here: https://itch.io/post/1044880 . In particular, this has at wind rate 5, i.e. 8-10m/s,

- Close-hauled 7 kt
- Beam reach 9.5 kt
- Broad reach 11 kt
- Running 8 kt
...
Heel angle
- Wind rate 5 - 11 deg

R. Braithwaite, "Notes to accompany drawings of the 32 gun frigate HMS Southampton", "HMS Southampton Stability Analysis", "HMS Southampton Velocity Prediction", 2009 
https://web.archive.org/web/20150417225544/http://richardsmodelboats.webs.com/32...

These are notes by a naval architect and model builder, applying some modern engineering analysis to a 1757 frigate, with some comparisons to historical reports on the ship. If I'm reading the stability analysis properly, you don't want to heel it more than 45 degrees or it will fall over.

Some questions: what exactly does close-hauled mean? How much leeway are these ships making? Are some ships typically faster with the wind on the beam, others with it on the quarter? (The French study has examples of both.)

I am working on tuning the sailing model towards these numbers. In my current development build I get, with wind 9m/s, the starting situation at "the world":

Close-hauled - 6.5kts  (wind one-and-a-half points before the beam)
Beam - 11kts
Quarter - 10kts
Before the wind - 7kts.

Probably the speed before the wind is about right (since I do not have royals) and the others should be a little slower.