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post #3 of Old 11-30-2007
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Originally Posted by JohnRPollard View Post
I thought I might begin a thread to discuss this topic. I hope the knowledgeable designers amongst us will chime in with their thoughts and correct any errors I may introduce below:

A recent post inquired about the Limit of Positive Stabilty (LPS) of a particular boat model. LPS, sometimes referred to as the Angle of Vanishing Stability, is a measure of a boat's ultimate stability. The LPS figure, expressed in degrees, is supposed to approximate the point at which a particular boat will heel so much that it cannot right itself. At that point, the boat may continue to roll upside down. In theory the sailboat will eventually self-right, usually by completing the roll through 360 degrees (assuming no downflooding, etc).

The ORC (Offshore Racing Council) recommends a minimum LPS of 120 degrees for off-shore racing. An LPS of 120 degrees would mean that the boat could heel an additional 30 degrees past a perpendicular 90 degree knock down, and still right itself (again, in theory, since LPS figures are static calculations which don't reflect dynamic variables such as sea-state, downflooding, loading, etc).

In the other thread I mentioned, JeffH made the following observation:

It struck me that JeffH essentially describes the vast majority of modern production boats.

Published stability tables for older production boats, as well as many newer ones, can be hard to come by. When I can find them (not all builders publish the LPS), it generally surprises me how low the LPS figures are. For instance, we are presently considering purchasing a larger sailboat for our family, and I was surprised to learn that the LPS of this popular 42 foot model was only in the range of 114 degrees. Our current 31 footer has an LPS of 139 degrees, which is among the lowest for all the models made by this manufacturer.

Looking at the hull form of the Bayfield 29...

...I would have thought the LPS to be higher than 105-110 -- it just looks like a more stable hull form than many of the modern production boats. So, lacking the LPS tables from a builder, how do we guage the suitability of a design for coastal or off-shore sailing? The figure of 120 degrees or better is considered desirable for off-shore sailing. What is a minimum LPS figure for coastal sailing?

Limit of positive stabiity is sometimes called the "point of no return." The boat heels over so much that righting arm shrinks to zero. At that point, once it heels further, which can happen by being tilted on a wave face at sea, the righting arm turns into an overturning arm and flips the boat upside down. A couple things to keep in mind:
The calc of this vanishing point is usually based on the hull form, but the cabintop can provide reserve buoyancy (provided the companionways is shut) and increase its value.
You'll routinely see pictures of capsized keelboats happily sitting upside down, their crew on the exposed hull bottom (or squirreled away inside). Because of hull form, a keelboat can be more stable upside down than it is right side up. That's partly because despite the weight of the keel, a keelboat's center of gravity typically is higher than the center of buoyancy when rightside up. What stops it from falling right over is that as it heels the center of buoyancy moves outboard, creating a righting arm. When a keelboat is upside down, the center of gravity is lower than the center of buoyancy, thus providing "good" stability. (Dinghies are typically the same, even moreso, as anyone who has turtled a dinghy knows.) Thus while a keelboat technically should be able to right itself, that isn't necessarily going to happen once it's upside down. Depending how much air has been captured in the hull (which affects overall buoyancy and the center of buoyancy as it rolls), it needs some external energy input to roll back rightside up. In storm conditions, waves can provide that.
The bottom line is that if hull form is exploited through form stability to provide a high vanishing angle, it typically means that it takes a lot of force should the boat become inverted to turn it rightside up again.
Steve Killing and I wrote about this in Yacht Design Explained, published by WW Norton in 1998. He could explain it all way better than I can, but that's a start.

C&C 27 Mk 1
Midland Bay Sailing Club

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