Originally Posted by Jaramaz
Jeff, here you are saying just adding displacement doesn't improve. In the sense that this is not always improves.
But on the other hand, (mass) moment of inertia is
The mass moment of inertia is a factor in the efforts to change a body (here boat) movement (around an axis). The higher MoI the more energy is required. Thus a boat with higher MoI will not be so easy to excite in movements as rollings etc - and then percieved as more stable (downside is then when the boat actually has been exited, then it take longer time to dampen the movements).
As the MoI is increasing with mass and size, both correlated to displacement, then one would generally expect higher displacement - higher stability (within limits).
Marchaj reasoned along these lines in his book "Seaworthiness -the forgotten factor". However, some of the conclusions in his book seems exaggerated. As said above, increased MoI has its drawbacks.
I think this is converging two separate ideas. You are correct that larger roll and pitch moments of inertia will slow roll and pitch acceleration rates. That comes at the price of larger roll and pitch angles. You are also correct that adding mass can add to the boat's roll and pitch moment of inertia. This is where the discussion gets more complex. The roll and pitch moment of inertia results from the collective moments of inertia of each mass based on its mass and that mass's distance (r) to the instantaneous roll and pitch axis.
By and large, since r is squared (or cubed depending on the calculation) it is changes in the distance to the instantaneous roll and pitch axis that has a greater impact on the the roll and pitch moment of inertia rather than the simple weight itself.
In other words, if we looked at two boats of equal mass, one which had all of its mass concentrated near the rotational axis and the other spread out into a bulb at the keel and a heavier mast, obviously the boat with the bulb and heavy mast would accellerate more slowly. In reality, even if we greatly added more weight near the rotational axis of the boat with concentrated weight, the accelleration rate would not be slowed to the point of matching the boat with the disbursed masses.
Going back to my earlier point, from the standpoint of optimizing motion comfort, the main factors are weight and buoyancy distribution and dampening, with overall displacement only playing a comparatively small role.
In terms of stability, "As the MoI is increasing with mass and size, both correlated to displacement, then one would generally expect higher displacement = higher stability."
I respectfully suggest that this is just plain wrong. Its true that if greater mass were added in a manner which did not change the center of gravity, or changed the center of gravity in a manner which is beneficial, such as added to a keel bulb, then adding weight would add stability.
But if that weight were added in the form of a heavy deck structure or mast, then that weight would decrease stability.
Which is why I said, "In and of itself simply adding displacement does nothing good for a boat, .... Weight does not automatically add to stability, weight does not inherently add to motion comfort.... Excess weight, especially in the wrong places hurts all of these things...."
As to Marchaj's book, "Seaworthiness -the Forgotten Factor", from everything that I know, Marchaj's basic science still remains correct and consistent with what we know today. If there is a shortcoming to the book, it is that much of the research was based on the boats that were available over 30 years ago when it was first written. In those thirty years, there has been a lot more research. And to one degree or another the lessons pioneered by Marchaj and later theorcists have been applied to improve the seaworthiness and motion comfort of the better sea going designs. So while the science is right, and the conclusions are correct for the type forms that existed at the time, some of his conclusions were too broadly applied and did not consider the subsequent design solutions intended to address the concerns that he raises in his book.