Conversion sail to power

I try to reason with parameters only from the laws of physics and, frankly, I cannot understand why adding or removing a mast (a tiny weight compared, for example, to that of the keel) could result in such "tremendous" changes in the roll period or in its amplitude.
Any theoretical explanation that even I can understand? Thank you very much in advance.

 

Polar inertia.

 

Certainly you can shorten the mast and use some sail in a beam sea to reduce roll. Many trawlers have this steady/stay sail to reduce roll.

I would like for someone to give a number of the amount of skin friction a boat would see poundforce per square foot at 8 knots.

Google "trawler with a mast" for 100's of picts

 

This boat has a retractable keel, 3.2 meters.

 

What you may think of as a "tiny" amount of weight is actually surprisingly heavy.
You can measure its circumference and wall thickness, and you know its length, now you can calculate its bare weight.
The wires are of known published weight per foot/meter, whatever, the weight of 2>3 hundred feet of it might surprise you.
Now we'll add in spreaders and a bunch of heavy stainless weldments and wire ends.
Oh, how about that big boom and all the fittings on it?
Take an estimated guess at the CG of the whole works and realize the total weight at the CG.
Multiply the total weight by the estimated height of the CG, (yeah, we could get all scientific and do an inclining experiment,) but you'll find out what a tremendous lever-arm that mast/rig exerts on the boat that resists being swung back and forth.
This is an easy example; hold a 1' piece of broomstick in your hand at one end and twist your hand back-an-forth quickly, now do it while holding a 5>6' piece.
The twisting of your hand and how quickly you can twist it represents the roll of the boat.
Milehog, in post #32 correctly summed up my long-winded rant in two words.

 

Yes, and the boat I was on when we lost the mast had a fixed keel of probably over 2 metres. It was still an uncomfortable and almost dangerous roll.

Increasing the moment of inertia to avoid uncomfortably fast rolling is a standard naval architecture technique, as used for example in cruise liners and even in battlehips like the Royal Navy's "R" class.

 

OK, thanks.

 

Yes, masts and rigging have to be heavy....top heavy.

 

The center of gravity of masts is normally below the midpoint, which is not top heavy. Masts that are not tapered have a higher CG, of course. However, the boom, winches,turnbuckles, and other hardware are all close to the deck.

 

"Close to the deck" understates the effect, the CG of the whole works, mast/rigging/spreaders/boom/winches, is still well above the CG of the boat.

 

I am not agreeing with your statement in #37 that "mast and rigging have to be heavy...top heavy". The rigging in general is not top heavy. As for the whole boat's CG, it is a combination of all the CGs. It would be facetious to say, for example, that engines make the boat stern heavy because their CG is aft of the center. A properly designed boat will have the CG at the right location. A mast on a sailboat makes all the movements slower, that is a basic principle of physics, not just boats. A simple example is a pendulum.

 

The actual inertial effect of the mast and rig on the roll of a boat is actually considerably larger than the mass multiplied by the height of the CG. When the boat is rolling the lateral acceleration at the top of the mast are much more than near the bottom of mast. The lateral acceleration along the mast is proportional to the height above the roll center. The combined effect is the inertial effect of the mast is proportional to the mass of the mast multiplied by the height of the mast squared.

For a mast with a uniform section along its length the moment of inertia about the bottom of the mast is 1/3 * mass * (total length ^2). The total length squared term is the reason a sailboat's mast can have a major effect on rolling. (The effect of gravity on the mast for static heeling is different. Gravity is constant along the mast, not proportional to distance from the rotation center. For a mast with a uniform section the moment for heeling about the bottom of the mast is 1/2 * mass * length * sin of heel angle.)

In addition to the inertial effects sails can provide a large dampening effect which can dramatically change the roll response, and may be the primary reason a sailboat underway close hauled or on a reach may be much more comfortable in a seaway than a rowboat or a powerboat.

 

I think that the concept of "moment of inertia" that you use has nothing to do with the one I use in my calculations. I use the moment of inertia, second moment, of a given area with respect to the axis of rotation in question. I don't know what the moment of inertia of a body is, which seems to be what you mentioned in the previous post.

 

Calculations of what? For calculations of torsional stiffness of a shaft, mast and similar the moment of inertia, second moment, of a given area with respect to the axis of rotation in question is used.

For calculations of the rotational dynamics of rigid bodies the seceond moment of inertia is used. In its general form the second moment of inertial is defined by an intergral. For a rod, mast and similar with constant cross section the integral can be simplified to the formula I gave.

Note that while the second moment of inertia formula is used in both torsional stiffness calculations with certain assumptions, and in rotational dynamics of rigid bodies calculations the physics are fundmentally different.

More about rigid body dynamics is readily available in introductions to the subject.