Schooner sail plan- centers of effort

[RHough]

Originally Posted by naval ark

It must be remembered that these are not scientific calculations - they are instead largely empirical guidelines. What we are actually trying to do is line up the dynamic centres of pressures for the hull and the sail plan, whilst heeled and upright, with full sail and reefed. As PAR stated, issues such as detailed hull design influence this dynamic balance as much as the sail shapes and locations.

So, 'what difference is there between a leg o' mutton Bermudian rig and any other rig?' Well, as the centres of areas are used with a certain amount of lead to give an acceptable approximation of real-life centres of pressure, as the shape, aspect ratio, efficiency, etc. of the airfoil changes so does the movement of the centre of pressure in relation to the geometric centre.

I know what we are trying to do. The question is, How does planform effect the lead?

Does a sloop need more lead than a schooner? Does a gaff rigged sloop need more or less lead than a Bermudian rig? How much more or less?

"To achieve balance, the correct lead of CE over CLP (=CLR?) as a percentage of LWL is 7-12 per cent for a schooner; 11-14 per cent for a ketch; 12-15 per cent for a yawl; and 13-17 per cent for a sloop or cutter." Dave Gerr (The Nature of Boats, p301)

On the 63 foot LWL in question the range of lead varies from under 2 feet for a yawl to over 3 feet for a schooner (if you only cite Dave Gerr).

Skene says 6% for cruising boats ... Herreshoff used 7% ... both completely out of the ranges recommended by Gerr.

Since it is not science what rule of thumb applies to adjust lead for planform?

Is there a method that is more accurate than the 0% to 17% of LWL I mentioned earlier? (short of the methods cited by Tim B)

I've been trying to come up with a more accurate method short of full blown aero and hyro dynamic analyisis with little success. Can you point me in the right direction to further my research? None of the recommendations that I have seen include any adjustment for sail planform.

"L Francis Herreshoff used to place the sailplan centre of effort of a conventional sloop to produce a lead of about 7 per cent ahead of the centre of lateral resistance. However, he listed several factors that might affect a sailing craft's balance.
(i) Hull shape. A deep, vee-shaped forefoot will obviously increase lateral resistance near the bows. However, in a yacht in particular you should also consider the lateral resistance of the heeled hull shape - it may be, for example, that at 15 or 20 degrees the bows have no grab, but the stern is beginning to put up significant lateral resistance.
(ii) Sharpness of the bows. As a sailing boat heels, there may be a large flow of water from the lee-side to the weather side of the bows. This tends to turn the bows up to the wind - by how much depends upon the sharpness of the bows.
(iii) Due to the shape is presents to the water, a wide shallow boat will tend to head up to the wind on heeling, while a deep narrow boat will tend to turn off the wind.
(iv) Increasing amounts of draft in a sail will tend to move the effective centre aft. (This is especially noticeable in the case of ice yachts, apparently.)
(v) Where the sail plan is divided into many sails, as in the case of a schooner, the effective centre of effort moves far less than when there is a single large sail, as in the case of a catboat.
(vi) The height of the sail plan. As a boat with a high rig heels, the centre of thrust on the rig moves outboard, again tending to turn the craft up wind.
How much allowance should be made for each of these factors? Think about each one and employ a sense of proportion, says Herreshoff, helpfully, for this is not mathematics but pure art."