| Well, in terms of addressing complexity, you certainly can take a big step
off the end of the dock (at low tide) with this one...or perhaps just try
a walk down the beach.
There are many ways to calculate a new ballast amount; it depends on your
objectives, which probably depend somewhat at least on how and why the
hull shape was designed. I'd suggest a review of Skene's Elements of
Yacht Design to put things in perspective before embarking wholeheartedly
on this venture, however. Here are some thoughts, though:
Will the ballast CG be at the same depth below the WL as before? Less
weight lower down could have the same righting moment, excluding any lift
effect of the keel section.
Is keel or bulb strut section shape an issue at all? (Will added length
increase lift, etc?)
One simple method (walk down the beach): Assume the hull was designed to
sail optimally at a certain WL. You need only to ballast the hull enough
to meet the original WL...the added ballast will equal the savings in hull
weight. It'll float on the DWL, though probably not sail at the heel
angle that it may have been designed for in a given set of conditions.
That may not be bad; it may simply not matter enough to matter.
4) Another less simple method (step off the dock): Assume the hull was
designed to sail at an optimal heel angle. Here the name of the game is
to balance the ballast weight and lever arm to reproduce the original's
righting moment. Options include:
1. Add ballast to bring total disp up to orig; shorten lever arm.
...Could make for a much stiffer boat.
2. Maintain orig ballast (and design, if wished); shorten lever arm,
but less than above.
...Match orig stiffness, but less wetted surface (less disp floats higher.)
3. Reduce the ballast some, and keep orig lever arm.
...Ditto #2 above.
4. Reduce the ballast more, and lengthen lever arm.
...Ditto #2 above.
Since changes in any single factor impact other factors and overall
performance (stiffness; roll and pitch rates; different lift and helm due
to immersed hull shape at each angle of heel, not to mention LWL....)
>>> I suspect sail area, beam, water line length, draught, and mast height
>>> are all factors.
There are a variety of calculations, many of which you can approximate
adequately yourself, shown in Skene's. Metacentric height, etc, etc.
Bottom line is that even a thorough analysis more often than not gets
tested and truly discovered for the first time only on the water. If it
was more of a science, they'd have figured out 12-meters and AC boats long
ago. Figuring out a good answer based on static stability figures often
doesn't translate predictably into dynamic characteristics. Aim for a
good approximation, and figure you'll tune the formula mid-season.
Sounds like a really fun problem to fiddle with!
J.
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