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Go Back   SailNet Community > Skills and Seamanship > Seamanship & Navigation
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Seamanship & Navigation Forum devoted to seamanship and navigation topics, including paper and electronic charting tools.


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Old 02-29-2012
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Conservation of angular momentum

I'm pretty sure I read it in Perry's Yacht Design book but I haven't been able to find the reference so I'm going by memory.

They were doing tank tests on hull stability when someone had the bright idea of putting a stick on the models to more accurately approximate real life.

They assumed that with the introduction of weight above the models would logically be more susceptible to capsize. What they found was the opposite.

In a purely static situation the boat without the mast would have the full lever arm of the keel to keep it upright.
In a real dynamic situation however the mass of the mast had a tendency to keep the boat from capsizing due to the conservation of angular momentum

Not totally intuitive but apparently true. People who have lost their mast have reported that their boat seemed even more prone to role subsequent times after the mast was cut away.

This has interesting consequences of course.
One I have never heard discussed is the possibly of hoisting something into the rigging to add weight.
It sounds counter productive as the goal is usually to reduce weight aloft. However maybe it is an appropriate technique in special circumstances.
For example would extra weight aloft stabilize a boat in certain kinds of rough anchorages.
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Old 02-29-2012
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Simple Inertia .... longer "roll period" interval.
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Old 02-29-2012
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I have a copy of "Desirable and Undesirable Characteristics of Offshore Yachts" that discusses this. You are right: people had previously thought of a capsize more like a static event with the large mass of ballast resisting, but found it is actually a dynamic event where distance and shape are important in addition to mass. Figure 3-1 in this book shows the contribution of the ballast, hull, and rig to resisting capsize in light and heavy yachts and the rig contributes about 60% and 70% respectively.

I took some related classes back in engineering school and am not sure about your weight aloft idea. Find a table of moment of inertia for different shapes and maybe plug in numbers to see what might be effective. For a "rod about it's end" like a mast, the formula is: I = (1/3)*M*L^2. The L squared tells you the length is the most important factor by far. Adding rigidly secured mass at the top, to move the effective M of that mast further out, thereby increasing L could add capsize resistance from an inertia perspective, but you sure wouldn't want it there when the boat is heeled far over and it's pulling it down further. So you'd want to calculate how much this idea would affect the overall roll resistance of the boat (i.e. Is it worth it? Is it possible to add enough weight to make a difference?) and how would it affect the boat's recovery from a capsize/knockdown (i.e. Is it counterproductive?) There are probably more issues.
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Old 02-29-2012
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Quote:
Originally Posted by DamonVT View Post
Adding rigidly secured mass at the top, to move the effective M of that mast further out, thereby increasing L could add capsize resistance from an inertia perspective, but you sure wouldn't want it there when the boat is heeled far over and it's pulling it down further. So you'd want to calculate how much this idea would affect the overall roll resistance of the boat (i.e. Is it worth it? Is it possible to add enough weight to make a difference?) and how would it affect the boat's recovery from a capsize/knockdown (i.e. Is it counterproductive?) There are probably more issues.
That was exactly what was thinking.
I seriously doubt that hoisting an anchor to the top of the mast in a storm will help prevent a capsize.

I was thinking in perhaps a very specific environment. Maybe in a wave-less anchorage that has a ferry going by every hour. Maybe a little weight aloft would dampen the periodic slop from the ferry.
Not sure it would but that was the type of scenario I was thinking of.
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Old 02-29-2012
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I never did very well in physics, but I can attest to the comparative stability with/without a mast. We crossed Lake Michigan with our mast down and stowed along the centerline (long story, but we were on our way down to the Gulf); the 5' swells on the starboard quarter had us rolling to the point that I was a little worried we might lose the rig. Not fun...
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Old 03-01-2012
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I have a degree in Physics and taught most mechanical engineering classes including Dynamics. Adding weight aloft does not make a boat more stable, it will increase the angualr momentum which will reduce it's roll rate, it will make it take longer to turn turtle. Depending on the freqency of the forcing function (the wave spacing, angle of attack, wind, boat speed, etc.) it might make the boat react less to the forces and feel more stable. A sailboat without a mast is more stable but can react faster to the forces applied to it, it may toss you off the boat because you don't react fast enough or hold on well enough. It has less tendency to turn turtle but can do it faster and will right itself faster. Stabilty and angular momentum are two totally different things. Stability measures the desire to stay upright, (the distance the center of mass is hopefully below the center of boyancy), angular momentum (the amount the mass is spread out), measures the speed the boat can change angle of heel.
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Old 03-01-2012
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One other thing related to this topic, Dynamic Stabilty, it enters in here too. It is the measure of the change in the location of the center of boyancy versus angle of heel, Multihulls have very high dynamic stability, the center of boyancy moves out very quickly and makes the boat stable even though the center of mass is above the center of boyancy. A standard hull has some dynamic stabilty, more beam, more stable. This is what can make a boat have two stable points, rightside up and pefectly upside down, or a cat be more stable upside down.

Also to get terminology correct, we should be using Moment of inertia instead of angular momentum, Momemt of inertia is the measure of the distribution of mass away from the center of mass (the mast being raised vs on deck, has it's center farther away from the total center of mass, therefore increasing the moment of inertia.)

Quick dynamics lesson. Momentum is mass times velocity, it's a linear thing, (acting in a straight line.) Conservation of momentum, means when something moving crashes into something not moving, they end up moving at an amount equal to the initial mass moving divided by the total mass moving after the crash. Conservation of angular momnetum is the same thing in a rotational sense, Moment of inertia before times angular velocity before equals amount after.
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Last edited by jheldatksuedu; 03-01-2012 at 05:09 AM.
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Old 03-01-2012
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What JH said.

Depending on the frequency of the wave train, a mast-intact boat may have a better reaction to that frequency that a mastless boat. Having anchored beam-to a small swell, I can attest that there isn't a lot of roll dampening in modern sailboats. Otherwise we wouldn't care or notice the defference much.

Note that the wave train frequency that sets up roll oscillations would be limited to some very specific frequencies. At the dock, jump off the side of your boat and time how long the side of the boat takes to go down and back up again (start the timer when the side of the boat is at its highest). For more accuracy, time over several cycles and divide the time by the number of cycles. The answer you get is the same as the wave train frequency that will set-up the worst roll oscillations of your mast-intact boat. (Actually, harmonics of that frequency would likely have a similar effect, e.g. a wavetrain frequency that was a third of what you measured.)

With your mast gone, the boat will have a higher roll oscillation frequency, and would react to a different wave train frequency, perhaps the one currently facing your just-dismasted boat.

If anyone who is taking their stick down wants to do this test before-and-after, it would be a great YouTube video.


Regards,
Brad

P.S. Of course, if you have forward movement, you could change your heading to alter the apparent wave train frequency. If hove-to with a sea anchor, changing to a smaller/larger sea anchor -- to add/subtract downwind drift speed -- could theoretically affect the apparent frequency, conceivably enough to matter. Perhaps a better and easier tact would be to let the sea achor act as a roll dampener by running some of it's (characteristically dampening) force to an off-centerline cleat, via a snatch block on the sea anchor line.

P.P.S. Theoretically, when not moving, altering the angle of the boat to the waves doesn't fully alleviate the runaway roll problem, since the underlying wave train has the same frequency, if not the same strength-per-individual-cycle. This is why people buy rocker-stoppers and other roll dampeners.
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Last edited by Bene505; 03-01-2012 at 10:33 AM.
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Old 03-01-2012
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Quote:
Note that the wave train frequency that sets up roll oscillations would be limited to some very specific frequencies.
So, say you are motoring in a seaway where the wave train (or a harmonic) is the same frequency as your boats roll rate. Would it reduce roll if you hoist some weight up the mast until the roll rate of the boat is different than the waves?
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Old 03-01-2012
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If I'm not mistaken, a tight rope walker uses a long pole to slow down his angular momentum. Same as a mast.
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