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12102007


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Yup... but I doubt it'd sink... A problem that many monohulls have...
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Telstar 28
New England
You know what the first rule of sailing is? ...Love. You can learn all the math in the 'verse, but you take
a boat to the sea you don't love, she'll shake you off just as sure as the turning of the worlds. Love keeps
her going when she oughta fall down, tells you she's hurting 'fore she keens. Makes her a home.
—Cpt. Mal Reynolds, Serenity (edited)
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12102007

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It seems to me that inverted form stability is importantand morbidly fascinatingbut only relevant in a small portion of the cases of boats that are knocked down past 90 degrees.
Anecdotal evidence (is there any other kind in matters like this where the sample is so small?) is that most boats knocked down below horizontal come up one way or the otherif they come up at alland right themselves. Often without masts and deck gear including deck structures.
I think the more interesting question is how to balance in a useful sailboat the attributes of initial stability, ultimate stability, ballast, beam, draft and hull volume. And for the boat owner/buyer, how to make a reasonable judgment of stability for themselves. While the screening formulas for stability are very simple they do give amateurs (most of whom won't be getting an IMS certificate) some notion of the factors involved. If the present screening formulas are inadequate maybe someone could come up with one that could be done with ordinary lines plans, boat specs and a pocket calculator. Or is there already such a formula?

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Quote:
Originally Posted by Nottoway

Quote:
Originally Posted by Jeff_H
That is an interesting formula seemingly pretty accurate. It came back with a LPS of 128 for my 10,500 lb 38 ft boat, which is about right.

JeffH / Nottoway / Diva,
Thanks for your commentary  I have found it to be very enlightening.
I tried fiddling with that US Sailing AVS formula, but got some results that didn't make a lot of sense to me. For instance, the AVS value I arrived at for our boat was negative!? Even when I convert this value to a positive figure, the value is far lower than the published LPS for our boat model.
I am now wondering if this AVS formula is quantifying a value that is actually different from the LPS? In other words, is the AVS value the point on the stability curve where the righting moment begins to decrease again, and the LPS is actually the point where the stability curve crosses the xaxis, i.e. the point after which the boat capsizes?
For illustrative/discussion purposes, here is the "Intact Stability Curve" for a common production boat, the Catalina 42:
The question rephrased: Are the Angle of Vanishing Stability and Limit of Positive Stability the same points on the stability curve? If the answer is no, then this might explain why many people are surprised to learn how low the AVS is for a given vessel (like the Bayfield in the other post that prompted this thread). Thoughts?
Last edited by JohnRPollard; 12112007 at 10:42 AM.
Reason: Added graphic

12112007


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LPS and AVS should be the same value, since they are describing the angle at which positive stability equals zero. The US Sailing number is only a rough approximation, which for my boat is pretty close to right. A proper LPS calculation calculates the vertical, lateral and longitudinal center of gravity and then models the center of buoyancy as the boat heels until it locates the angle at which the center of gravity is directly over the center of buoyancy which only occurs at three points, LPS, and level at rightsideup and upside down. There is also an IMS AVS which is calculated for all boats that are rated under the IMS rule. This number does not add for the cabin structure or deduct for rigging weight and so typically yields a low number for most racercruisers.
Jeff

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I think the problem with your calculation is that you are entering the draft of the keel; not the hull draft. For a Catalina 42 the hull draft should be somewhere in the range of 12 feet and that would give an AVS result somewhre in the 118130 deg range.
Use the following page for entering numbers; remember to use hull draft not keel draft:
http://www.sailingusa.info/cal__avs.htm

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Quote:
Originally Posted by KeelHaulin
I think the problem with your calculation is that you are entering the draft of the keel; not the hull draft. For a Catalina 42 the hull draft should be somewhere in the range of 12 feet and that would give an AVS result somewhre in the 118130 deg range.
Use the following page for entering numbers; remember to use hull draft not keel draft:
http://www.sailingusa.info/cal__avs.htm

Keelhaulin'
Thanks for pointing that out  yes, I was using total draft, not hull draft. I was actually working from the formula that Nottoway had linked to  I didn't realize there was an interactive site that would do the work for me. Very handy!
One problem, though, I know the total draft (hull and keel) of our boat, but not our hull draft without the keel. I could guess, but that wouldn't be very scientific.
Actually, I'm surprised that the formula does not want the keel draft  seems like that would be a major component in stability.
Also, I posted the Intact Stability Curve for the Catalina 42 just as an example. We don't actually own one. That curve was generated by Catalina Yachts and the designer, so I have to assume it's a more comprehensive calculation (such as JeffH described above) and reasonably accurate.

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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 5055 degrees. Maximum righting moment is being developed at 5055 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.
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Last edited by sailaway21; 12112007 at 09:23 PM.

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I see your point about maximum righting force. Certainly in the case of the Catalina 42 which is loosely an IOR hull form with a shallow keel depth, it would appear that maximum righting moment occurs near the point that the rail hits the water. This would seemingly be true for any boat where the center of gravity is near or above the waterline.
I somewhat disagree with the implication of your comments that "a traditional full keel boat may have its maximum righting moment at 90 degrees", "the traditional full keel boat will be almost impossible to keep inverted" and "modern designs....(read IOR)". The problem that I have with the two full keel statements is that keel type has little to nothing to do with the limit of positive stability, or the point at which maximum stability is achieved. Since the angles of positive stability and maximum stability are solely dependent on the location of the center of gravity and hull form, keels of almost all designs can achieve very large angles of positive stability and maximum stability. In fact as most 20th century full keel boats are actually constructed, they tend to have comparatively very heavy construction, heavy rigs, shoaler draft, and comparatively low ballast to displacement ratios, all of which would suggest a very high vertical center of gravity relative to the truly modern IMS/IRC derived designs, which tend to have deeper draft, light hulls and rigs, little flare amidships and no tumblehome and carry their ballast in bulbs deep below the rail. As a result, while traditional hull forms (which coincidently also tended to have full keels) typically had greater stability than IOR boats (which by no stretch of the imagination could still be called modern since the rule peaked in popularity over 25 years ago and died altogether roughly 20 years) these boats do poorly in terms of the angle of heel at which they achieve maximum positive righting moment or limit of positive stability as compared to truly modern IMS/IRC derived designs.
Historically, capsizes were very common in traditional full keeled vessels. Even discounting for the pre20th century use of internal ballast, by any reasonable metric one could not assume that a full keel boat is any less likely to capsize, and once capsized that it will remain inverted for any less time than a properly designed fin keel boat.
Respectfully,
Jeff

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Jeff, Sailaway, or anyone else with an answer,
Why does the US Sailing Screening Stability Value (SSV) formula use hull draft rather than total draft (i.e., including keel) for purposes of calculating the AVS? It seems counterintuitive to me.
Also, where did you get that "hull draft" value for your own boats? Did you actually go out and physically take a measurement (keel span  total draft = hull draft)? Or are these values available in a database somewhere?
Great discussion. Thanks.
Addendum:
Quote:
Originally Posted by Jeff_H
I see your point about maximum righting force. Certainly in the case of the Catalina 42 which is loosely an IOR hull form with a shallow keel depth, it would appear that maximum righting moment occurs near the point that the rail hits the water. This would seemingly be true for any boat where the center of gravity is near or above the waterline.
Respectfully,Jeff

Not sure what you consider to be a "shallow keel depth", but the stability curve that I embedded above is for the standard draft Catalina 42, with a published draft of 6'8".
Last edited by JohnRPollard; 12122007 at 03:14 PM.

12122007


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I guess it needs it to estimate the centre of buoyancy.

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