Bozeman, Montana, United States
Joined Aug 2003
3,457 Posts

Rudder size and the CLR and CE
re: rudder and jibs  In a multimasted ship, the rudder is more of a guide than a master. If the sail plan is balanced, ie. if the sail forces fore of the center of lateral resistance of the hull (CLR) are equal to the sail forces aft of the CLR, then a tiny rudder would be as effective as a large rudder. A baby can control a teettertodder if the 2 adults on the seats are the same weight. Conversely, if the forces are not balanced, then it would take a massive rudder to make up the difference  and the rudder would be hard over all the time, which will slow the ship. Slow ships have ineffective keels. They make lots of leeway on a beat, or any other point except dead down wind. So, for a good sailing vessel, you need to balance the forces.
The force of sails is dependent on the sail area and on the distance of the sail's "CLR" (actually called the sail's center of effort= CE) from the hull's CLR. The CLR is the fulcrum of the tettertodder, the CE's are the adults on the seats. This can all be calculated on paper, if you wish. Or, you can just put the boat in the water and see what happens. The seewhathappens method has the disadvantage that if the boat is unbalanced, its course will be set by the unbalance, and the capt. will be unable to sail the boat back to the launching area....been there, done that :) A symptom of unbalance is a ship that can tack, but not wear, or vice versa.

The paper method is pretty simple. The math is exactly analogous to finding the center of gravity of a real airplane:
1) Obtain or create a scale drawing of the ship's side view.
2) Mark the 1/4 chord point for each sail (the sail's CE), and for the hull+keel+rudder (the CLR). The 1/4 chord point for a rectangle (eg the hull) is just 1/4 of the length of the waterline aft of the bow. For a sail, it's trickier to find, but I just estimate the point where the sail's area is split 1/2 and 1/2, then split the difference between the 1/2 and the mast.
3) Measure the distance from the 1/4chord point of each sail to a specific point, eg. the end of the bowsprit. This is the lever arm for each sail. If you have a separate fin keel (as I always do), then treat the keel as if it were an underwater sail, ie. measure it's 1/4 chord point distance from the bowsprit. Ditto the rudder if it's big.
4) Multiply each sail's area by it's lever arm. Add up these sail "moments". Do the same for the underwater bodies to get the underwater moment.
5) Divide the total sail moment by the total sail area. The result is the summation CE for all the sails. That is, it's the distance aft of the bowsprit (or what ever you chose as the datum) where the sails all act together. It's the "center of gravity" for the sails (or center of lift to be precise). Ditto for the underwater bodies to find the summation CLR.

If the summation CE is exactly equal to the summation CLR (say, they are both 20 inches aft of the bow), then the ship is perfectly balanced.
More likely, there will be a difference. If the difference is "small", then the rudder will work to nudge the ship in the direction you want. You'll be able to tack and wear once you've had some experience sailing her.
If the difference is "big" then you will have to do something to move the CLR and the CE closer together. Big and small are relative to the ship; in other words, it takes some experience to understand what is too big. For my 2 and 3 foot hull ships, an inch difference is probably ok, but more than that, and I know I'm going to have to change something.
Easy changes: move the fin keel, if the ship has one, fore or aft so as to move the CLR to match the CE. Or, add or subtract jibs to move the CE. Or change the size of the rudder; this only works if you make the rudder bigger, to move the CLR aft, in my experience.
If you put the calculations all on a spreadsheet, you can tell what the ship will do when you reduce sail on a windy day. Changing sails obviously changes the summation CE. If you take off a jib, you will have to reduce sail on the mizzen, for example.
Note: You may not be able to wear even a balanced schooner, though, if the standing rigging prevents the booms from swinging out perpendicular to the hull on a run. This is the situation for my topsail schooner Aldebaran  she will only wear if she has her square topsails set....and the skipper is lucky with wind and wave :).

This calculation is for when the ship has a small heel angle. If the ship gets hit by a gust and heels over, then she will turn into the wind due to the asymetrical thrust of the bow wave. Your calculations won't be much use then, nor will you have much control over her course. The solution is to do as the real ships did, namely, reduce sail in a blow.
Gusts are one time I find a big rudder helpful: it may allow me to control the ship's course enough to get her back to land so I can reduce sail area. And in a calm, a big rudder may allow me to scull the ship back to land; a tugboat is a more elegant solution :). Incidently, a long, shallow rudder works better sculling than a narrow, deep rudder. The former more closely approximates a whaleboat's sweep. It's all about moments :)
