Neil;
I don't consider your original reply to my post to be nitpicking. You are right and CG can be above CB - and it is for many types of vessels. I was thinking of the typical keelboat that we sail when I was writing, and for that type of boat I would stand by my post - the CG in normally below the CB. Center of Buoyancy is the geometric center of the water displaced by the hull, so it must, by definition, be below the waterline. (and in response to Dwight's question, yes if the displacement of the boat exceeds the total buoyancy of the hull, the boat sinks and the CB can be thought of as being WAY below the waterline.) On our typical keelboats the mass of the keel is well below the waterline and lowers the CG to a point below the CB. On my 38 the mass of the keel is approaching 45% of the displacement of the boat, and other systems like engine, tankage, batteries, etc are also concentrated below the waterline. It is true that the CG of the rig is more than 25 feet above the waterline, but the total rig is considerably under 7% of the total displacement, with all other parts of the boat are less than 5 feet above the water. I'd guess the CG of my boat is perhaps 18 inches below the WL (roughly at the bottom of the keel stub, while the CB is perhaps 6 to 8 inches below the WL. Worst case for a keel boat would be a keel-centerboard configuration. Perhaps someone with a 34/36 or a 37/40 would care to weigh in on this, but I think a common keel-Centerboard boat has a considerable mass of keel in the stub/trunk, as well as a weighted centerboard to keep the CG low. But in my experience keel-centerboard configurations tend to be quite tender with the board up, and more tender than conventional keels with the board down. I mentioned why in my original post. Our boats, with the CG below CB, display static stability. Boats with high static stability are self-righting tend to have ultimate stability (the angle from which they can right themselves) well in excess of 100 degrees. All the examples in your attached diagrams were in the 120 - 150 degree range, IIRC. In truth, several types of boats have the CG above the CB. Dinghies (which are by definition non-self-righting) are the case shown in your stability diagram attachment (though I note the information on the CZ curve shows a keelboat with CG below CB.) Catamarans are another prime example. Woe be onto you if you pitch pole a cat, they are more stable upside down than right side up. Dinghies and cats are what is known as metastable. They are statically unstable (CG above CB) and would fall over except for the form stability of the hull. As they try to fall over, the CB shifts to the low side and creates the righting moment that keeps the boat upright. But metastable boats have an inherent problem in that the angle of ultimate stability (the angle where the relation of CG and CB will cause them to turn turtle) is limited to the point where water will come into the boat and cause a loss of buoyancy - and that angle is always less than 90 degrees of heel. Your point about the static stability of a cruise liner is also valid, they too are probably metastable, with the proviso that the situation is probably not as dramatic as you picture. Suppose a cruise liner of around 20,000 tons displacement and a 10 meter draft. Because of the hull cross section, it is reasonable to assume the CB is 4 M below the waterline. Below the waterline are all the ship's heavy mechanical systems - engines, sewage, water desalinization and distribution, power generation, steering engine, kitchens, HVAC , refrigerators, freezers, and storage holds. Centered and at the bottom level will be the fuel tankage. Such a ship will use 20 tons or more of fuel per hour, 500 tons a day, 3500 tons for a week, so the fuel tank has quite a bit of impact on the CG. Abaft the fuel tank and down low are water ballast tanks, and the water ballast counts toward the CG calculation but isn't part of the displacement of the ship. Many ships also have ballast tanks that are filled with seawater to offset the stability lost as fuel is consumed. All told, about half the ships displacement is below the waterline. What about the 6 or 7 decks - call it 20 to 25M - above the waterline? Mostly air. Large public spaces inside smaller decks above the Promenade Deck (#3?), an atrium, dining rooms, pools and sports deck. Half the displacement, but with a CG only 1/3 the way up - call it 7 M. So the CG of the heavy stuff is 5 M below WL, and the CG of the topsides is 7M above the WL, for a net of 2 M above WL or 12 M above the keel. The cruise ship is still not statically stable, but the CG is only about 6 M above the CB so it is much less unstable than you originally suggested. But I gotta admit, every time I see one of those suckers leaving for the open ocean, I'm amazed that they don't just flat fall over. Isn't marine architecture fun? Rick Brass From: CnC-List [mailto:cnc-list-boun...@cnc-list.com] On Behalf Of Neil Gallagher Sent: Thursday, December 05, 2013 4:50 PM To: cnc-list@cnc-list.com Subject: Re: Stus-List Now Stability - was List halyards again( 10 aloft = 1 on the rail ) Marek: Picture a large cruise ship: its draft might be 10 m, so its vertical center of buoyancy is a little more than 1/2 way from the keel to the waterline, say 6m above the keel. The center of gravity is not only above the center of buoyancy, it's well above the waterline, sometimes 20 m above the keel, yet unless it happens to buzz too close to an Italian island, it will stay upright. Or picture a small sailing dinghy without anyone on it, the CB again is below the waterline, while the CG is well above, but they don't capsize until the sheets are pulled in. A yacht's form stability is the same as a ship's; for sure, adding a keel to a yacht improves the stability by lowering CG, but it does not necessarily put the CG below the CB, in fact it usually doesn't. (There is a point called the metacenter, which is an imaginary point on centerline through which the buoyancy force always acts, that is the point which must stay above the CG for positive stability...but now we're getting deep into naval architecture.) Check out the illustration below: http://www.troldand.dk/en/?The_Yacht:Stability#.UqDzkvIo5Ik Neil Gallagher Weatherly, 35-1 Glen Cove, NY On 12/5/2013 3:05 PM, Marek Dziedzic wrote: Neil, this cannot be. As Rick said, if the CB was below the CG, the boat would instantly turtle, at the slightest provocation (the state of equilibrium at rest (flat on the water, with the mast upright) would be inherently unstable). Btw. this is why we carry around the heavy keels (to move the CG down). Btw. some newer (acrobatic) dinghies might have the CB and CG very close or inverted (especially when the crew is onboard) and are unstable at rest (they get stabilised by speed and force of the wind), but this is a completely different story. Marek _______________________________________________ This List is provided by the C&C Photo Album http://www.cncphotoalbum.com CnC-List@cnc-list.com
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