Is there a well-defined relationship between Cg and motion?

Hi all,

I'm curious to understand if there's a good way to predict the motion of a vessel (say a barge) in the ocean given a Cg. It's my understanding that, for a given lower Cg, the motion in most axes improves - sort of how ocean wind turbines use a very deep ballast to keep upright.

Taking aside that swells will vary and produce an impact, is there a good way to understand how Cg may improve or change Pitch, Roll, and Heave motion? Put another way, I suspect if you had a wind turbine with a 3000ft deep ballast, it would not pitch/roll very much at all.

Less concerned about Sway, Surge, and Yaw, also because intuitively I don't think the Cg has a big impact on those.

 

Yes and No. There is a broad correlation between a vessels GMT (Transverse Metacentric Height) and its natural Roll period. Since KG (distance above keel of the Cg) is a factor in GMT, it affects the roll period (T), but is not the only factor. There is a similar effect for GML (Longitudinal Metacentric Height) on natural Pitch period. KG has no effect on natural Heave period (not exactly true, but let's not confuse the simple case). Surge, Sway, and Yaw are generally not periodic except when forced.
Note the emphasis on natural. Most motions in operations are not natural, but are forced by the seaway. That is a whole other chapter in the textbooks.

 

To follow up on JEHs post.

The natural periods of motion are determined by the attributes associated with a restoring force. By that I mean, Roll, Pitch and Heave.
These are the 3 motions that are influenced by the hull shape/size.

Rolling - GMT
Pitching - GML
Heave - Aw

The hull shape, and mostly the ratio between under water volume and the waterplane area, influences these 3 natural periods of motion, in association with the location of the KG.

And then some.
Seakeeping is terribly complex.