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Old 09-27-2012
dacap06
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Re: Moment curves

Bob,

I've been catching up on my SN reading and found your series of posts here. Might I suggest you work this material into a blog post? There are many beyond just SN readers who would find it fascinating!

What you said makes perfect sense and I think I can visualize it. Tell me if I have this right:

In a sense, the area curves you discuss show the distribution of buoyancy forces from the displaced water volume with respect to the boat's centerline and distance from the cutwater. In short, those curves show the areal distribution of buoyancy at different heeling angles (or roll).

These same data can be used to determine the position of the CB so that a static righting moment can be calculated for a given roll. To see how it affects the static position of the boat, begin by assuming a particular angle of heel for a stationary boat in flat water. Do an iterative calculation that rotates the pitch of the boat such that the CB moves toward the CG horizontally. Recalculate the buoyancy area generated by the displaced volume and therefore the new position of the CB. To get to the final solution, lather rinse, repeat (i.e. iterate) until the longitudinal position of the new CB is the same as the longitudinal position of the CG. Doing so for various angles of heel allows you to find static pitch as a function of static roll.

T. P. Donnelly
S/V Tranquility Base
1984 Islander 30 Bahama