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

[jehardiman]

Originally Posted by fferhani

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

Ok think of it this way. The center of flotation is the axis in pitch where, when a moment is applied to a free floating hull in balance, that the new submerged volume is equal to the now emerged volume, and the moment couple of these two volumes is equal to the applied moment.

Lets start with a rectangular barge with a beam of 1, a length of 2, and a draft of 0.5 floating in a fluid of density 1 in level trim. It has a weight of 1 and it is obvious that the CG is in the center. Now we move a small weight a small distance forward on the barge. The total submerged volume does not change. The bow pitches down picking up buoyancy and the stern rises losing buoyancy, the size of these two volumes is identical because no weight changed on the barge. As the bow pitches down, the new immeresed wedge generates a pitch up moment, and the new emerged wedge aft also generates a pitch up moment (actually a minus pitch down). For this simple shape, it is obvious that the location where the new water line crosses the old water line is exactly in the middle of the barge because, not only the volume but the shape and CG's of the two wedges are identical.

Now lets consider a body also with a beam of 1, a length of 2, and a draft of 0.5 but with a triangle for a forebody and a semicircle of a stern and we will fix the CG again in the center by tucking the stern up. Again we move a small weight a small distance forward on the barge. This time, if the barge was to rotate around the midships, the volume of the emerged wedge would be larger than the volume of the immersed wedge and have a much larger moment (if you want the math, I can show that but it will have to wait until after work). We therefore need to adjust the axis the barge pitches around until both the immersed wedge and the emerged wedge are the same volume AND the moments generated between the two is equal to the moment generated by moving the weight. By inspection it can be seen that we need to move the pitch axis aft to compensate for the larger waterplane aft. And this is why Brewer states that the center of flotation is generally aft of the CG.

Edit; Xpost with Eric, go see his stuff.