# Relation mass gyration and upwind perform.

Discussion in 'Sailboats' started by Erik de Jong, Sep 22, 2009.

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### Erik de Jongsail freak

I have a class 40 which has a maximum allowed draft of 3.00 meters. In some oceanic races it is allowed to start with an open 40 without draft limitations. I want to make a second keel with, lets say, 4 meters draft and 25% less ballast weight, in this case the righting moment remains the same but the boat is several hundreds of kg lighter.
Now my point:
the mass gyration of the ballast is the distance between rotation point and CG of ballast to the 4th exponent (d^4) multiplied by the mass (m)
Instead of 121500 kgm4 we will have 288000 kgm4 (almost double). This must have a major influance on the upwind performance of the boat.....
I only don't see how to make an estimation of that... can anyone be of any help in this matter? Has there been (model) researches?

2. ### Paul KotzebuePrevious Member

Do you mean "mass moment of inertia" instead of "mass gyration"? If so, the units are kg*m^2, not kg*m^4.

Also, the keel is just one component of the boat itself. You need to compare the mass moment of inertia of the entire boat before and after the keel modification, or analyze the effects of keel changes on the entire boat's mass moment of inertia. In the general case it is possible that big changes in the keel mass moment of inertia will not have a big effect on the entire boat.

You're in for a grueling calculation no matter what ....

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### Erik de Jongsail freak

yes that is what I mean, I mixed up the two, sorry. English is not my native language....
You are right it is kg*m^2.

The main reason that this is on my mind is that when the anchor is hanging on the bow of my parents cruising yacht, you feel the differance! it is only 35 kg on a 46ft ketch. As soon as we remove the anchor it sails more quitte, more relaxed. We do not find a differance in speed, but we are talking of 35kg on a 14 ton boat. The ballast difference I'm talking about will be approx 300 to 350 kg on a boat of 4.5 ton (6 to 8% of the boat weight).
I think the only way to find out is to build that second keel and hang it under the boat. Luckily it is only one bolt... and easy to reach

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### PetrosSenior Member

Do I understand you correctly, you think there will be a change in performance with a change in the rotational inertia of the boat? It seems to me that if you have more rotational inertia, the boat will not tend to pitch and porpoise as much in a rough sea. That would be good I suspect because the sail and keel will not be changing as much relative to the wind and current, but you will have more pounding on the hull. Also all the pitching must take energy, so any time you can reduce the pitching, it seems to me that would mean there would be more energy (drawn from the wind) for driving the boat forward. But this might be lost if there is more drag on the hull from it being driven deeper at each swell.

IT would be a very complicated calculation, but it might be simplified by making gross assumptions...calculate how much power it takes to pitch the craft back and fourth with an assumed wave frequency, and the difference with the reduced pitching. there are other factors as well, sometimes certain hull shapes have more drag than others in rough water vs. calm.

On smooth seas it does not seem to me that there would be much difference since you do not have significant rotational displacement, so there would not be much affect on the rotational mass.

I know on aircraft pitch damping and rotational inertia are critical factors in dynamic stability calculations (unstable aircraft tend to kill people). I have never seen it applied to boat hulls with regard to performance. Interesting thoughts though.

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### Raggi_ThorNav.arch/Designer/Builder

I agree with Paul here.
It ain't that simple.
If you heel at approx 90 degrees and the center of flotation then is close to the cg of the boat without the keel, then you have the same rightning moment with the new keel. At normal sailing you will have much less stability since the boat is much lighhter and probably also with a narrower waterline.

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### yipsterdesigner

was just gonna mention an alu anchor may compensate inertia changes, ah but waterline comes up eh..

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### Erik de Jongsail freak

@Ragnar,

I did put some numbers for the keel changes to make clear what kind of change I have in mind (I did not make any calculation yet). Ofcourse it is necessary to look at the whole stability range of 0 deg heeling to 180 deg heeling.
In this paticular case it becomes also more complicated because of the 750 kg allowed waterballast which is situated close to deck, not really attractive with a 90 deg heel. But these are all things I can solve. My problem is the mass inertia influance (I hope it is the right word).

Usually when we design sailingyachts, we arrange the heavy items (eg batteries, tanks, life raft) around the rotation centre. The ballast is by far the heaviest item on board and we want to put it as deep as possible. That is in matter of mass gyration not the most attractive place.

What I am afraid for is that the boat will pitch more than before.
Take for example a closer look at an IACC yacht I'm not sure of the exact numbers but it is a 5 tons boat with 18 tons ballst very deep underwater. It doesn't look good when the boat moves in choppy water. To me it looks like the boat is rotationg around the ballast bulb instead of around it's own hull.

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