Metacentric height and roll period VS inertia

[wroc]

Hi,
I am designing a sailing scow. I know the theory of CG and CB and metacentric height, and resulting roll period. However, differing distribution of mass for the same CG must have an effect on roll period, right?

In the example of my sailing scow, which will have rectangular sections, if ballast is placed along the chines between sides and bottom, the ballast weight will all be quite far outboard from the longitudinal axis around which the boat will roll. This will have more inertia than if the ballast were placed along the longitudinal centre of the hull. How much does this affect roll period?

This hull form will already have large initial stability, and ballasting it will increase this stability further. I have other reasons for favouring this hull shape, but I'm trying to minimize uncomfortable, snappy rolling, if possible.

 

[jehardiman]

I know the theory of CG and CB and metacentric height, and resulting roll period. However, differing distribution of mass for the same CG must have an effect on roll period, right?.

Kinda-sorta, but different.... The GM (i.e. waterplane inertia and CG) determines the natural roll period. The Mass Inertia retards the roll rate; not the period, natural or otherwise. Think of it like a rotary torsion mass system with a small damper under a forced input; increasing the rotary mass inertia will cause the magnitude of a forced or natural roll to change, but not necessary the period.

 

[wroc]

Kinda-sorta, but different.... The GM (i.e. waterplane inertia and CG) determines the natural roll period. The Mass Inertia retards the roll rate; not the period, natural or otherwise. Think of it like a rotary torsion mass system with a small damper under a forced input; increasing the rotary mass inertia will cause the magnitude of a forced or natural roll to change, but not necessary the period.

Ah! I think I see. Roll period will be the same, but forces will need to be applied for longer, or with greater force, in order to induce movement. So overall the boat will be less responsive to outside forces, and have less roll motion (all other things being equal) than a boat with less rotary mass inertia. This is a good thing. Thanks for your answer.

 

[jehardiman]

Yes, but you have to watch for natural resonance. As a wave moves across a hull, it causes a force which starts the roll. It also means that that roll has to be arrested by gravity and the waterplane before the vessel starts to roll back. Single wave, single roll and then the vessel will oscillate at its natural frequency until all the energy is dissipated.
Get the selection of GM and inertia linked to a wave near the natural frequency and you can start a feedback loop depending on how much damping is in the system because the energy becomes additive (i.e. the vessel continues to roll due to its large inertia until not only the wave surface, but gravity forces it to rotate in the return direction, actually increasing the amount of roll on the 2nd oscillation). This is when many vessels can "roll the gunnels under". Anti-roll tanks and bilge keels are used to provide enough damping to prevent this.

 

[wroc]

Yes, but you have to watch for natural resonance. As a wave moves across a hull, it causes a force which starts the roll. It also means that that roll has to be arrested by gravity and the waterplane before the vessel starts to roll back. Single wave, single roll and then the vessel will oscillate at its natural frequency until all the energy is dissipated.
Get the selection of GM and inertia linked to a wave near the natural frequency and you can start a feedback loop depending on how much damping is in the system because the energy becomes additive (i.e. the vessel continues to roll due to its large inertia until not only the wave surface, but gravity forces it to rotate in the return direction, actually increasing the amount of roll on the 2nd oscillation). This is when many vessels can "roll the gunnels under". Anti-roll tanks and bilge keels are used to provide enough damping to prevent this.

OK. I don't really have the capacity to calculate this accurately, but if this effect starts to manifest itself, I'll move ballast around. This will be a sailboat, so the sails and rigging will provide damping, in addition to the leeboards. I expect the worst condition to be with boards up and sails down, but usually if there's waves (and wind), I'd have sails up, if only a reefed riding sail. I've rolled the gunnels under at sea before, on a well-proven design, and avoiding this condition was only a question of changing the parameters somewhat. Sails, trim, course, and so on.