"Center of Buoyancy" question...

Hello,

I recently purchased a beginner's guide to yacht design, and I have a question:

If the boat is in perfect trim, and weight is added fore or aft, does the boat rotate about the "center of buoyancy" as it pitches? There are some definitions that are vague in the book, and this was one issue that confused me.

Thanks.

Robert

 

That's a question of mythical proportions. Each hull model, depending also on how it was build, behave differently. For example, a clipper bow will pitch aft of the center of bouyancy. A plumb bow with a wide stern forward of it. Another influence is the moment of inertia of the boat. This includes the rigging. A tall heavy mast slows the movement of the boat, but also changes the axis of it. I distrust most of the fast and eay formulas that claim to answer all conditions. Experienced designers always study the behavior of similar boats. The most important thing to understand is that boats have dynamic centers of bouyancy. It changes continuosly. Water is a moving medium. I hope this helps and encourages you to keep on studying.

 

Gonzo, thanks for the reply; when I'm confronted with issues like this that confuse me, I usually extrapolate the issue to an extreme; in this case, I assumed a boat that was sinking, and that let me visualize the canter of buoyancy shifting forward as the bow dipped into the water. Now, this same book also stated that the center of gravity was always inline (read: over) the center of buoyancy. I started thinking about race car dynamics, and how the "roll center" of a car was partially dictated by the cg, and by the suspension geometry. In relation to boats, how would this "roll center" not *always* be the center of buoyancy, since it was always inline (in a vertical plane) with the cg?

This book claimed that there is a midpoint of the waterline (I forget the actual term he used...darn it) that was actually the pivot point of the "teeter-totter" (boat) as you weighed it fore and aft. I assumed this to mean the point on the waterline directly above the center of buoyancy, but that didn't make sense either...it just seems like the boat would always "roll" about the center of buoyancy itself; isn't that the point that has the hull in total equilibrium in the water? I can't seem to achieve any clarity on this, and it drives me nuts!

Robert

 

Robert

You have to consider the boat in either a static or a dynamic condition as its behaviour changes with motion and/or in wind/waves. Your book described the static condition.

The centre of buoyancy is the centre of gravity of the displaced water and has three coordinates. The one that you ask about is the Longitudinal Centre of Buoyancy – the LCB. The centre of gravity of the boat – the LCG – lies vertically above the LCB when the boat is upright in still water.

When the boat trims, due to adding a weight or moving one, it rotates about the centre of area of the waterplane which is termed the Longitudinal Centre of Flotation – the LCF (the term you couldn't remember). Let’s say that the boat has a draft of 5 feet ford and aft and the LCF is 40% of the length from the after end. A weight moved forward then induces a trim of 10 inches, this means the change aft is 40% of 10 = 4 inches so the change forward is 10 – 4 = 6 and the drafts become 4’ 8” aft and 5’ 6” forward.

This is true for small angles, for anything greater than 5 degrees the full calculation finding the real LCB of the trimmed hull and other properties is necessary. These take days to do manually, are straightforward with a good computer program but are not necessary for everyday conditions.

When a boat moves through the water it creates a wave train and the calculated centres change position. When there are waves in bad weather the shifts are even greater but the conditions themselves rapidly and chaotically change and the boat motion becomes very complex. This is why only the standard static conditions are usually found. Designers achieve safety by establishing compliance with known traditional values. The s… hits the fan when new designs introduce novel, untried features and it is ”back to the drawing board.”

The distribution of weight on the boat has an effect on the speed at which these changes occur. Suppose you held a steel rod with your hand at the mid point and the rod had two sliding weights on it that could be fixed in position. If the weights were close to your hand you could flex your wrist quickly but it becomes more difficult, and slower, as the weights are fixed near the ends.

All the boat motions cause the axis of rotation to move towards the boat centre of gravity. But you don’t want that to happen as it only occurs in the extreme case – a submarine.

Hope this has helped clarify things

Michael

 

I think many of these books spend too much time on static calculations. They are very valuable, but do not represent the behavior of a boat underway. Mike is correct in his observation that "The s… hits the fan when new designs introduce novel, untried features". That is the main reason for tank testing. It is cheaper than finding out after the boat is built. There are easier, more economicla ways of testing models. Herreshoff made a rig to compare hull shapes which was very simple. It works on the principle of a scale. Two models of hulls to be compared get attached to the ends of a beam. The beam is attached from the center to a line leading to and outrigger on a boat. Herreshoff used a 20' launch of his. You can change speed, wave conditions and angles of heel while comparing the relative resistance of both hulls. It is a great way to test for modifications. This ties in with your question of centers of bouyancy, center of gravity and the interactions between them. You can make models of different shapes, tow them and observe the changes in behavior. Seeing is believing.

 

The "point" of rotation of a boat when pitching is about the Centre of Flotation (the longitudinal centre of area of the waterplane). Of course, this is a moving target, as it changes all the time during poitching. But it's a good start ;-)

 

I think that a flat bottom boat will illustrate the dynamic changes on hull underwater shape. It goes from flat and horizontal when level to a vee section when heeled over. I know it may seem overwhelming, but it takes time to figure it all out. Next time you go boating your theoretical knowledge it going to make you observe the behavior of the boat. You'll find yourself analazing everything. The best part is when numbers and theories match what you see.