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Old 08-10-2010
48' wood S&S yawl

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Jeff, are Hull Draft and Displacement Volume in the formula measured in meters and cubic meters? I think my computer cut off or mangled the end of your post.
Feet and cubic feet IIRC. As long as you're not mixing systems, the relation should be the same.

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Old 08-11-2010
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A couple very quick thoughts here:

I want to comment on RGSCPAT's comment which said, "
"The sails, mast, and rig also have a big role to play in making the boat stable and sea-kindly. The wind pushing against the sails is generally a good, stabilizing force; in general a sailboat in a good breeze is going to roll less and be more comfortable than a motorboat or the sailboat with its sails down, to give a simple example. With the sails up, some weight aloft can be a good thing."

I think I understand the intent of this quote but would like to see if I can break it into its component parts for clarity. I would agree that the sails, mast and other rigging components have a big impact on stability and motion in ways that are both good and not so good. The weight of the sails and rig, have a negative impact on stability across the entire range, meaning that, all other things being equal, the heavier these components, the more the boat will heel or pitch in relation to any given roll or pitch inducing force (wind or wave induced) and the slower that the boat will be to right itself.

But that weight has an impact on motion that is a mixed bag. An increased weight of the sails and rigging will cause a boat to roll and pitch more slowly, but to roll and pitch through a wider angle. In a single wave induced knockdown, that added weight will initially slow the roll rate of the boat, and depending on the length and steepness of the boat, can decrease the likelihood of a capsize. However, because this weight is carried above the roll axis, the boat will continue to roll further into the trough and depending on wave shape, and LPS roll far enough to dip its mast into the next wave or roll past its LPS and so actually be at greater risk of a capsize.

The other aspect of this is the impact of having sails up. The force of the wind in the sails, (and the counteracting side force of the water on the keel) as well as the forces generated as the sails are swept through the air and keel through the water will act to dampen (surpress) roll motion, and so the boat will typically have a more comfortable motion when the sails are full. This is a separate set of forces and a separate discussion from those forces which are related to the mass of these components. Dampening turns out to be an extremely significant component in motion comfort when considering roll and pitch. This has been an area that has been widely studied and the current trend towards hull forms with finer bows and their center of buoyancy located further aft in the boat, as well as deeper bulb keels and taller but lighter rigs, eliptical cross sectional shapes, and moving weight out of the ends of the boat, are all a part of an effort to improve dampening relative to roll and pitch forces, and therefore improve motion in terms of simultaneously reducing roll and pitch accelerations and angles.

I am not precisely certaib what happened that part of the formula does not show up, but here is the AVS formula from US Sailing. US Sailing has stopped using this formula and is relying on STIX instead. I personally like this as a rough approximation since it includes more of the critical factors than the previous "Capsize Screen Formula" that US Sailing developed back in the 1970's. The input does need to be metric since the constants in the formula are intended to convert these forces into a rough approximation of AVS.

Screening Stability Value ( SSV ) = ( Beam 2 ) / ( BR * HD * DV 1/3 )
Where;
BR: Ballast Ratio ( Keel Weight / Total Weight )
HD: Draft
DV: The Displacement Volume in cubic meters.
DV is entered as pounds of displacement on the webpage and converted to cubic meters by the formula:

Displacement Volume in Cubic Meters = ( Weight in Pounds / 64 )*0.0283168
The Beam and Hull Draft in this formula are in meters.
These values are entered in feet on the webpage and are converted to meters before SSV calculation.

Angle of Vanishing Stability approximately equals 110 + ( 400 / (SSV-10) )

Also Hull Draft is a bit confusing. In the text, which is no longer available online, this factor was explained in more detail. I do not recall why, but I originally thought that the HD was intended to be the actual draft of the vessel, but later I concluded that it represents the depth of the canoe body of the vessel. I actually put together an Xcell spreadsheet which calculates this very quickly. Using the depth of the canoe body on my boat results in a surprisingly close approximation of the actual calculated AVS of my boat using the empty boat numbers. This may be sheer coincidence since the formula does not include some of the key elements that would impact LPS (AVS) for example, My boat has a pretty heavy rig for such a light boat. If I went to a carbon fiber rig but then used that weight to add a second fuel tank equal to the weight savings, the displacement and calculated AVS would not change at all, but the real AVS would change dramatically.

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Curmudgeon at Large- and rhinestone in the rough, sailing my Farr 11.6 on the Chesapeake Bay

Last edited by Jeff_H; 08-11-2010 at 09:25 AM.
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Old 08-11-2010
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So, to estimate the screening stability angle and angle of vanishing stability, the trick seems to be getting a good guess of the boat's "hull depth", because a moderate difference in this value makes a noticeable difference in the result.

Trying to estimate these numbers for three boats, I get

Catalina 30
10.8333 beam (English), 3.302 (metric), 10.903 (m^2)
4250/10250=.417 ballast ratio
1.42 ft hull depth = .434 meter (guessing from sail plan diagram)
10250 lbs disp / 64 * 0.0283168 = 4.535, ^1/3=1.655
36.45 CSV, 125 degree AVS

Schock 35
11.75 beam (English), 3.581 (metric), 12.826 (m^2)
4500/10000=.45 ballast ratio
1.9 ft hull depth = .579 meter (complete wild guess)
10000 lbs disp / 64 * 0.0283168 = 4.245, ^1/3=1.6417
29.98 CSV, 130 degree AVS

Ericson 35Mk 2
10 ft beam (English), 3.048 (metric), 9.29 (m^2)
5000/116000=.431 ballast ratio
1.9 ft hull depth = .582 meter (guessing from sail plan diagram)
11600 lbs disp / 64 * 0.0283168 = 5.0882, ^1/3=1.71997
21.536 CSV, 145 degree AVS

And just for fun I get a CSV of about 1500 and an AVS of 110 degrees for a Sunfish.

How does this compare with any published values?
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