Limit of Positive Stability (LPS)

[JohnRPollard]

Originally Posted by Idiens

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

I can accept that. But I would have thought that the US Sailing AVS formula generates distorted results because it does not factor keel/ballast depth.

Still, when I guestimate our hull draft, I get AVS results that range from 132 degrees (1.5 foot hull draft) to 152 degrees (2 foot hull draft). I'm fairly confident our hull draft is within that range (we draw 4'10"). The designer's puplished LPS for our boat is 139 degrees.

So I am impressd that this formula seems to work anyway, given that both JeffH and I have tried it out and produced results within the expected range. What I'm struggling with is WHY it does work given that it seems to ignore keel draft?

[sailaway21]

I have not played around with it John but I'd hazard a guess it is because immersed hull is a far more important variable then the keel depth below the water, or draft.

[jrd22]

JohnR- I couldn't find a hull draft for our boat either. Using the actual design drawings I was able to measure fairly accurately the hull draft. I came up with SSV of 26.73 and AVS of 133.9. I am going to call Ted Brewer and ask if he has the actual values tomorrow. This is for a Brewer 40 PH.

John

[JohnRPollard]

Originally Posted by sailaway21

I have not played around with it John but I'd hazard a guess it is because immersed hull is a far more important variable then the keel depth below the water, or draft.

Sailaway, I find that proposition intriguing, and counterintuitive. If your suggestion is correct, that might explain why the LPS/AVS for the Catalina 42, and other similar relatively flat-bottomed modern designs, is so low.

But, with that in mind and looking at some photos of JeffH's boat hauled out (that he has posted in the photo gallery), I am surprised his LPS number came out as high as it did. The hull form of his boat seems to emphasize low wetted surface -- very different from our boat. Our boat is more old school -- the hull is down deep IN the water, rather than floating atop it like the wider, flatter modern designs. [This is not intended as a criticism of Jeff's boat, just an observation.]

Originally Posted by jrd22

JohnR- I couldn't find a hull draft for our boat either. Using the actual design drawings I was able to measure fairly accurately the hull draft. I came up with SSV of 26.73 and AVS of 133.9. I am going to call Ted Brewer and ask if he has the actual values tomorrow. This is for a Brewer 40 PH.

JRD, that's interesting. I have some drawings too of our boat, but it's somewhat of a guess as to where the hull ends and the keel begins. Viewed in athwartship cross section, ours has the fairly traditional wine glass profile, so the transition from hull to keel is very gradual. And the ballast is bolted externally to a fairly deep keel stub. So I am left wondering where US Sailing gets that value? From the owners? If so, there could be a large fudge factor on some boats.

I'll be curious to hear Mr. Brewer's thoughts. Maybe you could direct him to this thread and see if he might be willing to post some comments? If not, I look forward to hearing from you what you learn.

In the meanwhile, I'm going to run the numbers on our boat again, then I will post the figures and how they were derived. Maybe others would be willing to do the same with their own boats and perhaps the comparisons will make for interesting discussion...

[Jeff_H]

I am not sure why the formula is written the way that it is. When I tried to enter a deeper canoe body the AVS initially got smaller, but when I put my boat's draft in, the number came back at 358 degrees, obviously not a realistic. I also experimented with changing displacement, entering my boat's displacement when fully loaded, which I have actually measured when it was in the travelift. By increasing my displacement by 3000 lbs, my stability dropped by 5 degrees.

If I think about it, I can rationalize it this way, on a boat with a shallow canoe body, as the boat heels the center of buoyancy moves up the topsides of the boat more quickly than a boat with a deep canoe body. Therefore the CG is would be over the center of buoyancy at a smaller angle of heel. Thinking about why increasing displacement reduces the AVS, similar to above, the deeper a boat floats on its side the closer to its keel the center of buoyancy is likely to be and so the sooner that the CG will be above the CB. The reason that the formula suggests that a shallower canoe body than mine would have less stability is that a similar boat with a shallower canoe body would float deeper for its displacement and so would also capsize at a smaller heel angle. What the formula does not consider is freeboard. My boat has pretty low freeboard, and so would tend to have a lower AVS than a boat with higher freeboard.

What ever else you can say, the 128 degree AVS number is pretty close to the actual number for my boat, which may simply be a coincidence since my boat is such an anomaly in the design world.

With regards to John Pollard's comments on my boat, it is what I was saying earlier. Light, shallow canoe body boats do not necessaily have small Limit of Positive Stability angles. That misconception goes back to the days of the IOR when light weight was associated with boats that had very high vertical centers of gravity. My boat actually has pretty high ballast to displacement ratio and a very low center of gravity compared to heavier boats of that same era. Newer IMS/IRC influenced designs have even smaller LPS angles still, way narrower than my boat and most traditional cruising designs.

Jeff

[jrd22]

I was unable to call Ted (work sure gets in the way of important business!), might have a chance tomorrow. I'll ask him if he would be interested in reading the thread and shedding some light on the subject.

John

[sailaway21]

I will confess to approaching this subject from the experience of a ship's officer. That is not all to the bad, with exception granted to the notion of stinkpotters. What is apparent to me though is that, within our discussion, we are to some extent approaching things somewhat backwards. We should first approach such matters from the theoretical and then consider the practical.

Consider two opposing ideas. One holds that a stiff ship is desirable, the other that a tender ship is desirable. The stiff ship responds well to a press of canvas and heels much less under that load. She also has a very fast rolling period. The tender vessel will heel more readily and may well dip her rail much sooner under much less press of sail. So the vote goes to the stiff ship right? Not necessarily. We don't sail generally upon calm seas and the ship's motion cannot be ignored. This is particularly so when running. The stiff ship is much more prone to synchronous rolling given her already short rolloing period while the tender vessel will be far less likely to engage in such potentially catastrophic behaviour. All of which merely points out that things are not quite as simple as they may appear.

One area Jeff and I will surely agree upon is the perverting nature of racing boat rule making. The notion that racing derived hull forms has improved the breed is open to question, with the debacle of IOR coming readily to mind. Readers of this forum are undoubtably concerned more with seaworthiness than ultimate speed, although the stating of such is in no way meant to obviate the interaction of speed, comfort, and seaworthiness. The only reason for the mentioning of it is the persistant advertizing of the race it/cruise it sort that may imply there are no trade offs. In my opinion, seaworthiness may be the factor that goes by the wayside.

To truly discuss the subject, a grasp of basic principles of naval architecture is required. You may purchase PNA, Principles of Naval Architecture, but I'm afraid that most of us are not really up for any refreshers in calculus. I'd recommend a seemingly odd choice that will provide a more than rudimentary knowledge of the terms required, that at the same time, will not require more than a pleasant couple of hours reading to plainly explain the factors and forces we're dealing with here. "Stability and Trim for the Ship's Officer" by John LaDage and Lee Van Gemert, the second edition of 1956 is a wonderful book of some only 200 hundred pages. It's published by Cornell Maritime Press. I recommend you purchase the second edition off Amazon for a mere pittance rather than the new edition, updated by my late fellow instructor at the USMMA, Bill George. This in no way should serve to diminish Bill's efforts, it merely reflects the fact that CMP is getting the princely sum of $50 for the latest edition and our purposes can be well served by the older editions.

Within it's covers you'll find the terms of CG, CB, and the metacenter well and clearly explained. More importantly, the understanding of righting arm, GZ, and righting moment, GZ x Displ., carefully explained. There are many common misunderstandings of stability that are easily and understandably eradicated by a quick reading of this book.

Along with that book I'd recommend C.A. Marchaj's "Seaworthiness, the forgotten factor". While updated in 1996 it is somewhat dated, the author's prejudices are perhaps a bit heavy-handed, but coupled with the knowledge gained from LaDage it gives an excellent jumping off point for the fascinating discussion of sailboat design. A discussion which has prompted me to pull out my long neglected copy of Chappelle's "The Search for Speed Under Sail".

In answer to John Pollard's question I can only mention that displacement means little without reference to the locations of CG and CB. As in Jeff's case, it is of utmost importance as to where the added weight is loaded. A factor not mentioned yet, in the discussion of stability at large angles of heel, is the waterplane. As the boat is loaded, or heeled, the waterplane changes affecting possibly both CB and CG. If the boat is loaded deeper the effects of tumble home may obviate even a lower CG. Tumble home will also reduce righting arm at large angles of heel compared to a slab sided or even flared hull boat. The shift in buoyancy on a slab sided boat when heeled is not proportional due to the consideration of deadrise. Imagining a ballasted log might help with the understanding of the concept.

I should confess also that i have not gone into the AVS link provided and must do so soonest if I am going to participate further here. Hopefully tonight's Christmas party and a compliant wife will make that possible yet this evening.

Great thread in what promises to be a great forum.