Owner, Green Bay Packers
Join Date: Sep 2006
Location: SW Michigan
Posts: 10,318
Thanks: 0
Thanked 0 Times in 0 Posts
Rep Power:
13
Jeff,
I think I was unclear in my post and, perhaps, in your's as well what terms we are talking about.
The righting arm GZ is the horizontal measurement between the vertcal vectors of G and B. I'll leave out any discussion of GM as we're discussing stability at large angles of heel. As the boat is heeled, B moves outboard towards the immersed side. This intuitively makes sense as we are immersing more hull to one side. The more hull we immerse the further outboard B will swing and the larger GZ will become. For most vessels, at or near deck edge immersion, GZ or righting arm is the greatest, but not all vessels. At that point, we have the maximum hull volume immersed to the heeled side and have thus moved B as far outboard as it can go. As the deck edge immerses, we lose buoyancy to the heeled side, and B begins to move inboard. For sailboats of certain design deckhouse structure can obviate this and will certainly influence it as heeling continues. We are not at LPS, but we are at the point of diminishing stability.
It can be seen by this why increased freeboard adds more positive stability after the angle of deck edge immersion and how tumble home will reduce potential stability. Increased freeboard also increases the range of stability. Tumble home reduces stability at all angles after immersion of the tumbled home portion of the side. Conversely, hull flare will generate a larger righting moment at large angles of heel despite it's other drawbacks. Deadrise is desirable only to the extent that B is initially high. If G is comensurately high, there is little advantage in terms of ultimate stability. If G is kept low, as in a traditional full keel boat, the effective raising of B by deadrise is desirable.
A traditional full keel boat may in fact achieve maximum righting moment at 90 degrees of heel. In fact, due to deckhouse shape as well as the position of G they will maintain a GZ, or righting arm well past deck edge immersion and perhaps have only 30 degrees or so in the danger zone with negative GZ. To your point though, I think it is more common for modern boats to at minimum begin to rapid lose GZ after deck edge immersion, and for most the maximu is developed at about that point. The problem with more modern designs dependant on form stability (read IOR) is that G has risen, thus at deck edge immersion, or soon thereafter, righting arm begins to dissipate rapidly. Due to their large danger zone of negative stability they will remain inverted for dangerously long periods of time. Whereas the traditional full keel boat will be almost impossible to keep inverted. Designs that rely on form stability too much show deceptive GM numbers which are not indicative of the boat's performance ar large angles of heel, particularly after deck edge immersion.
Just looking at the graph above in JohnRPollard's post illustrates my point (wish I'd looked closer earlier) and is perhaps a source of much confusion. Maximum positive stability is not at 114 degrees as labeled, it is at approximately 50-55 degrees. Maximum righting moment is being developed at 50-55 degrees and it decreases from there. 114 degrees is the point of vanishing stability or negative GZ. This Catalina has about a 65 degree danger zone and, once capsized, will have difficulty getting back on her feet. The most likely reason being that G is at or near the waterline.
“Scientists are people who build the Brooklyn Bridge and then buy it.”
Wm. F. Buckley, Jr.
Last edited by sailaway21; 12-11-2007 at 09:23 PM.