Large keel to displacement power boat?

[philSweet]

Just a couple of observations regarding TANSL and Daquiri's exchange. It is a bit off topic. If a boat is rolling in a seaway, it's roll period is the same as the forcing function - ie the wave encounter frequency. Adding something such as a mast won't alter the frequency at all in a particular sea-state. It can only change the magnitude of the roll. This restraint on frequency response makes the effect of changing the moment of inertia a lot more tractable, but far from trivial. If the natural frequency of the boat's roll is slower than the wave encounter frequency, the effect from slowing it down further is pretty easy to estimate. However, if the natural frequency of the boat's roll is quicker than the wave encounter, slowing it down will be hard to analyse and the motion of the vessel is likely to change in complicated ways.

And I think what TANSL was trying to point out was that the POLAR inertia is not the flavor of interest. It is a property of the extrusion's cross section.

 

[TANSL]

And I think what TANSL was trying to point out was that the POLAR inertia is not the flavor of interest. It is a property of the extrusion's cross section.

That's exactly what I say. Sorry I have not been able to explain.
I have doubts about what others say because of my poor English, but for me it is clear that the moment of the boat relative to the longitudinal axis of rotation (which passes through the center of gravity of the waterplane area) has nothing to do with the polar inertia of the mast.
Regarding what you say, it seems clear that the movement of the waves generates the movement of the ship, which has a natural frequency. The frequency of the waves can, as appropriate, increase or decrease the amplitude of motion of the boat, which will continue to have the same frequency (imo). What do you think of this?

Clarification: I know this is not, I've greatly simplified the issue, the phenomenon is more complicated, for example due to the mass of moving water dragged by the hull. I wanted to raise the idea that the frequency of ship motion is independent of the frequency of the waves.

 

[philSweet]

As long as the ship is one rigid unit, and the sea state is dominated by periodic waves, the ship's motion should settle to a regular periodic function with the same frequency as the wave encounters. What varies is the phase shift. Now depending on the specific situation, it may not take too much of a perturbation to throw the response off a lot. And the settling time to return can be quite long. So if you happen to be in one of those corkscrew conditions, You're probably not going to find a comfortable, low-motion place to store the seasick people.

see part 3 here for some explanation - http://en.wikipedia.org/wiki/Harmonic_oscillator

 

[daiquiri]

Just a couple of observations regarding TANSL and Daquiri's exchange. It is a bit off topic. If a boat is rolling in a seaway, it's roll period is the same as the forcing function - ie the wave encounter frequency. Adding something such as a mast won't alter the frequency at all in a particular sea-state. It can only change the magnitude of the roll. This restraint on frequency response makes the effect of changing the moment of inertia a lot more tractable, but far from trivial. If the natural frequency of the boat's roll is slower than the wave encounter frequency, the effect from slowing it down further is pretty easy to estimate. However, if the natural frequency of the boat's roll is quicker than the wave encounter, slowing it down will be hard to analyse and the motion of the vessel is likely to change in complicated ways.

And I think what TANSL was trying to point out was that the POLAR inertia is not the flavor of interest. It is a property of the extrusion's cross section.

That's correct, Phil. I was just discussing the influence of the added mass and inertia of the mast on the roll period of the ship. Once the roll period is known, the natural rolling frequency of the ship is also known (f = 1 / T ), and that's where things become interesting and complex at the same time. If you are also able to estimate the damping coefficient of the hull, then the classical mechanical vibration theory can be used to estimate the behavior of the ship in a seaway, for a given roll-excitation moments at given wave-encounter frequencies.

It is just a naval-specific application of the classical vibration theory, which is covered pretty well in this Wiki page: http://en.wikipedia.org/wiki/Vibration
The resulting characteristic curve of roll behaviour of the ship will be very similar to this one: http://en.wikipedia.org/wiki/Vibration#mediaviewer/File:Forced_Vibration_Response.png , where peak rolling amplitude will coincide to the excitation frequencies which are multiples of the previously mentioned natural rolling frequency of the ship.

Cheers