# Beam to height ratio for motoryachts

Discussion in 'Boat Design' started by ccme, Jul 22, 2007.

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### ccmeNew Member

Hi,

I was wondering if there is a ratio for the beam/or deck cabin width and it's maximum height. Let's say we have a beam of 25 ft. To what level above water this max beam can occur? Mean a 75 ft beam boat will not have a beam/cabin width of 75 ft on for example 10m above waterlevel.

Thanks.
Martin

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CCME; There is no simple ratio that will indicate permissable height of cabin. This a matter that requires considerable calculation. Try Wikipedia or google to learn about "metacentric height". Briefly; that is about the relationship of the distances between the center of bouyancy and center of gravity of the boat. You may study this concept with any of the several books that address the subject. Try "Skenes Elements of Yacht Design" for a start.

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### lewisboatsObsessed Member

Maximum beam usually occurs at or just a bit below the shearline. Not only does this keep the center of gravity lower but the maximum ultimate stability is reached before the cabin etc gets near the water. The shear is usually defined in this case as the line where the deck meets the hull and anything above is bulkworks or rail or whatever. Most powerboats have some kind of deck around the cabin space to allow movement forward and aft on each side of the cabin...thus making the cabin narrower than the shearline. If the boat has the maximum beam below the shearline...it has tumblehome...which lessens the ultimate stability but is used for asthetic purposes.

Steve

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### ccmeNew Member

Thanks messabout and lewisboats

Thanks for your help.

Do you know of any figure from experience, like "I've never seen a motor yacht with a beam of 25 feet that has this width of 25 feet of cabin (or else) on a higher level then 25 feet above waterline".

Thanks again.
Martin

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### alan whiteSenior Member

The cabin height is not the only issue. cabin width and shape will contribute to establishing self-righting calculations. Cabin length obviously matters as well. What type of boat is important to consider. The hull shape will either support or not support a tall cabin. Ballast comes into play.
It is impossible to set a limit based on any formula unless a hundred other factors are given values as well.
Most all design formulae are simple and based on very few parameters. Cabin height and shape will affect several of these. As the cabin goes higher, so does the center of mass and the tendancy to pitch, roll, capsize, suffer windage, and carry sail lower. Yet a higher cabin will also assist in self-righting by enclosing submerged volume lower.
A hard and fast formula isn't used for height alone, but the cabin shape can produce data that becomes a variable in another formula.
If you are designing a boat now and wish to calculate "How high?", you need to figure out what increasing height has done to raise the boat's center of mass and what changes have occurred in its stability curve, consider the value of inverted bouyancy, changes in pitch and roll, and whatever other factors (such as rig changes on a sailboat, or bridge/highway clearances on a power boat) and go from there.
I have many times designed-doodled sailboats with very tall cabins that were also very short fore and aft in order to achieve a pilot house steering station.
If I design a tall cabin, I must also make it short, so I have to eliminate superstructure elsewhere or lower that considerably to compensate.
A St Peirre dory I'm working with now (design stage) has a narrow hull and not a lot of ballast. Since a full standing room cabin is out of the question I consider a short pilot house that allows standing at least in one small area, but the rest of the accomodations, instead of the customary 4 1/2 feet of height, go down to four feet of even less. This maintains my center of mass and windage, only slightly increases roll/pich characteristics, and if totally enclosed, assists in self-righting.

Alan

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### lewisboatsObsessed Member

I've seen it...usually with a name like "Pacific Princess" and the like. Most of the large cruise ships have superstructure that extends straight up from the shear line and can be as tall as the beam is wide...or even a bit more. They also have the length and displacement to carry the load and they don't just walk but RUN away from bad weather... more due to the sensibilities of the passengers than to any fault in the seaworthiness but I know I wouldn't want to ride out a hurricane in one of those.

Steve

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### ccmeNew Member

Thanks Lewisboats

Have you ever seen a motoryacht with a beam of 25ft and a superstructure of 25ft width on a level of 25ft above waterlevel?

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### alan whiteSenior Member

I've heard that question before somewhere... and there it is again.

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### charmcSenior Member

25' x 25' x 25'?

Hi, Martin,

This is what it would look like, at least proportionately. I suspect the max beam on this vessel is about the same as the overhang of this structure.

The limitation is stability, and the details can get pretty complicated: superstructure material of construction, hull material, weight and location of machinery, tanks for consumables, etc, etc, etc.

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### alan whiteSenior Member

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### charmcSenior Member

I guess it also depends on the kind of boat.

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### HalcyonJunior Member

Boat Height - Windage

Superstructure will contribute to righting moments at the higher angles but of course that assumes it is watertight.

A consideration also has to be windage.

If the boat is going out to sea away from sight of land then an allowance has to be made for a squall or steady wind from a sudden storm hitting the boat beam on.

The IMO calculations for this use the profile of the boat above the water with the pivot being half the hull depth below the water line. I seem to remember the wind speed was force 8, but I’m writing this off the top of my head, I’ll be near my reference library later so I’ll update you then. Unless someone else can help me here? The force created from the wind coupled with your stability curve will give you the resulting angle (there is a similar calculation produced for sailing yachts when assessing stiffness).

Again this is off the top of my head but I believe the formula for wind pressure is called Martins Theory (?? I have a bad memory for names) and the centre of effort would be the centre of area of the above-water profile.

The resulting angle should not allow any down-flooding or exceed the suggested 16 degrees, which ever is soonest. I think the MCA would prefer 10 degrees. If you stick to 10 degrees as a maximum it not only gives you a safety factor but the calculation is also easier. You would have to advise me of any US requirements.

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