Is the center of flotation in line vertically with the center of gravity?

Discussion in 'Boat Design' started by fferhani, Sep 12, 2010.

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fferhaniNew Member

Hello,

I am doing some reading on boat design. Most definitions of the center of flotation say that it is the center of gravity: this definition, this one, and this one. However in his Yacht Design Primer Yacht Designer Ted Brewer states that the Center of Flotation is "the pivot point about which the boat changes trim" and that this point is located "somewhat abaft the Center of Buoyancy," which itself is "in line vertically with the center of gravity."

I don't understand why there would be "a pivot point about which the boat changes trim" and if such a pivot point indeed existed I would expect it to be aligned with the center of gravity and the center of buoyancy. Do you know if such a pivot point exists and where it is located?

Thanks!
Fabien

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The centre of floataion, CF or CoF, is the centre of gravity of all the area, or centroid, about the waterplane of a ship. In other words, a 2D plane.

See below:

The centre of buoyancy/gravity is about 3D (length, breadth and depth), not 2D planes (length and breadth). The CoB and CoG are always in line. The CoF is not always inline with CoG, it varies with hull shape, on the water line, in plane view.

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WillallisonSenior Member

Fabien
The Centre of Flotation is the centre of the area of the waterplane - a section taken horizontally through the boat at the waterline.
It is indeed generally a little aft of the LCG and LCB, both of which are always in line. Or put another way, if they're not, the vessel will always trim to bring them back into line.

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WillallisonSenior Member

ahhh... see your fingers are faster than mine John...

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ancient kayakeraka Terry Haines

The center of buoyancy (CoB) is determined by the underwater shape of the hull. The center of gravity (CoG) is the balance point of the mass of the boat and its contents. They are unrelated.

Let's define the useful term Metacenter; when the boat is upright the CoB is on the centerline of a symmetrical hull. When the boat heels slightly the CoB shifts to one side, and a vertical line through it will cross the centerline at the metacenter.

The greater the vertical distance between the CoG and the Metacenter the more stable the boat. Do not be tempted to think of metacenter and CoG as the pivot and bob of a pendulum; the boat does not pivot about its metacenter *.

Imagine a nice perfectly round dry log floating high in the water; its CoG, CoB and metacenter are all on the axis and the log has neutral stability so it will roll helplessly if disturbed. Now slice the log in two along the axis and let one half float in the water. The CoG is offset from the axis but the CoB and metacenter haven't moved. So it will now float with the flat side uppermost; it has stability.

It should be noted that the relationship between the metacenter and CoF is usually maintained on for small heeling angles.

Returning to the mystical pivot point mentioned at * above, that the boat rotates about as it heels. The boat would rotate about its CoG if it were spinning in free space. You might expect it to rotate about the CoB when it’s in the water, but that ignores the effect of its own mass which is centered at the CoG. The pivot point is between the CoG and the CoG.

6. Submarine TomPrevious Member

That last sentence is sure to confuse...

-Tom

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sorenfdkYacht Designer

Well, don't believe everything you read on the 'net. The first three references you give have little or nothing to do with yacht design or naval architecture. Ted Brewer, on the other hand, is an icon (at least in the states...)

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jehardimanSenior Member

Fabien; If you tell us what type of boat design you are interested it, we could point you to some good basic texts were all the proper terms will be defined and calculated, like Skene's, Gerr's readable works, or Principles of Naval Architecture or Ship design and Construction if you really need the technical standards.

I shudder at the thought of looking up technical definitions on the internet without some background text; i.e. the third site you listed gave 8 blurb examples of the term, most of them out of context and some in direct conflict with each other.

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fferhaniNew Member

Thanks Jehardiman!

I just want to understand key concepts in sail boat and motor boat engineering because I went on a day sailing trip last month with friends and found boat engineering very interesting. Right now I am reading the fourth edition of Ted Brewer's Understanding Boat Design, which I checked out from the library. I do look some concepts up on the internet when I do not understand them in the book. If you have better boat engineering references to recommend let me know!

Fabien

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fferhaniNew Member

Thanks Ad Hoc! Do you have the one or two previous pages too? I think they would help me understand how x1 and y1 are relevant. What publication did you get this from?

Fabien

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From 'Basic Ship Theory'
KJ Rawson & EC Tupper

Any good library should have this, or book shop/website.

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fferhaniNew Member

OK so it seems pretty clear that the center of flotation is the center of the waterline area. However I still do not understand why, as Yacht Designer Ted Brewer claims in the fourth edition of his Understanding Boat Design book, "on normal sailing hulls the center of flotation is somewhat abaft the center of buoyancy," and why "it is the location about which the vessel changes trim as the weights are moved, like the center of a teeter-totter".

Does anybody understands why the center of the waterline area should have those properties?

Thanks!
Fabien

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MikeJohnsSenior Member

Adding onto the information already posted. You'll even find a lot of definitions that confuse these. Probably because Naval Architecture and Physics have different definitions.

Importantly a vessel trims dynamically around the CFPlane CG arm and statically around the CG CB arm.

When a CG CFP arm exists then there is a dynamic pitching moment with heave. This effect is well illustrated in a drop test of a model.

You easily can easily conceive some shapes that would lead to extremes of this principle for example some ULDB sled racing sailboats.

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lewisboatsObsessed Member

Because the Center of Flotation, being only a slice of the hull with no depth does not account for the volume of water that it occupies whereas the Center of buoyancy, which includes volume, does. Picture a long narrow triangle (plane of flotation)...the center will be near the base. Now, in profile this is an infinitely thin line so...add volume to it, not with a straight line but with a curved line that curves down sharply near the tiny point, rounds down to the physical center of the length of the triangle then slopes upward towards the base. Looking at the profile of THIS shape you will see that the center of flotation of the profile is significantly forward of the center of flotation of the triangle. The combination of the two...along with the shape the skin connecting all this together is given (which will be a continuous blend of the straight sided triangle as it curves to meet the curved "keel" will finish up creating the volume of the figure. The center of buoyancy is the culmination of all this and will be forward of the plain center of flotation of the triangle. Being as the water supports volume which contains weight...if you shift the weight the boat's trim will adjust to match the weight shift. The point along the waterline where this shift will occur coincides with the center of flotation which is fixed. The center of buoyancy shifts with the center of gravity to support the hull at the new trim angle. If you walk forward in a dinghy...the bow will go down, the stern will go up...the total volume displaced will remain exactly the same and the axis around which the boat rotated is the longitudinal center of flotation. Unless the boat is asymmetric side to side...the centerline is always the transverse center of flotation.

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Eric SponbergSenior Member

To all,

Remember we talked about all this on the "Center of Flotation" thread:

http://www.boatdesign.net/forums/boat-design/center-flotation-calculation-implications-30857-18.html

"The Design Ratios," which is the series of "lectures" that I gave in that thread, can be accessed and downloaded on post #264 on the last page. The series begins with the center of flotation, and goes through all the design ratios in a series of 12 chapters, or lectures. You can go back through the entire thread, too, to see the contributions from the other writers in the thread.

Eric

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