# wind heeling moment equation

Discussion in 'Boat Design' started by Bassoom, Jun 25, 2005.

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### BassoomJunior Member

hi everybody:

i need to calculate the wind heeling moment for an offshore jacup for a range of heel angles.

is there is anybody knows an equation to calculate the heeling moment which is afunction of heeling angle?

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### dougfrolichSenior Member

Heeling Force=Righting Moment/Heeling arm
Righting Moment=Weight of vessel x Righting Arm(GZ)
Righting arm for SMALL ANGLES =GM sin(heel angle)
BM=moment of inertia of WaterPlane/(diplacement lbs./64)
GM=Center of gravity to Metecenter
BM=Center of bouyancy to Metecenter

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### BassoomJunior Member

hi there:
thank u for your response, but i need an equation to help me in my calculations.
i have the heeling arm equation:

heeling arm = .17*10^-6 AV^2*cos^2(heel angle)/Displacment

i need something like that for the heeling moment.

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### Raggi_ThorNav.arch/Designer/Builder

I think you have it all.

The preassure from the wind is approx 1/2 x density of air x wind speed squared
1/2 * RO * V^2

The force is preassure x area

The arm is the distance from the center of teh underwater profile to the center of the profile over water.

Isn't that close enough?

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### BassoomJunior Member

Yes i think that is enough

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Hello, could you please tell me what 'RO' stands for
Thanks

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### daiquiriEngineering and Design

You have to start from the codes your design will have to conform to. In the Oil&petroleum industry, the most important codes are those of the API (American Petroleum Industry), NORSOK (Norwegian petroleum industry) and the ISO (codes 19900 through 19906). The ISO seem to have adopted the best of the two worlds (American and Norwegian) and is probably set to completely substitute the later two in the future. Of course, there are also rules issued by DNV, Lloyds, GL etc. The choice of the rules which the design will stick to will depend principally on what is written in the design contract.

All these rules and standards give you the procedures, charts, tables and formulae for estimation of wind loads, which you will have to stick to. If you don't, the design and calculations will not be approved by the authority or by the client. So the first step is to carefully read the design contract and see what does it require from you.

Cheers

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### TANSLSenior Member

From what I understand Bassoom not want to know the force of the wind, but the heeling moment for various values ​​of the angle of heel.
May it be correct to say that the heeling moment equals the displacement multiplied by the GZ value at each heel angle?

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### Olavnaval architect

ro, also rho, is the greek letter ρ which usually stands for the density, like in this case.

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### Olavnaval architect

Not necessarily so. This is only true if the vessel is at equilibrium at this angle of heel. The heeling moment may be larger, causing the vessel to roll to a greater angle (until equilibrium is reached), or lower, thus making the vessel roll to a smaller angle (again: until equilibrium is reached).

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### daiquiriEngineering and Design

Hi TANSL,
this is what I read in the opening post:
As Olav said. You are correct that at the point of equilibrium the heeling moment has to equal the righting moment (as Dougfrolich has pointed out too), but what if the heel angle is required for a given wind force? In that case the wind-resistance calculations will have to be performed too.

Cheers

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### TANSLSenior Member

I agree, what I say is true only when the ship is in equilibrium. But at that moment, there is no doubt that the "wind heeling moment" is equal to what I say.
It all depends on what it is exactly what Bossoom needs to calculate.

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### NavalSArtichokeSenior Member

I doubt Bossoom has been waiting for 8-1/2 years for the latest replies to his query. Check the date of his original post.

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### daiquiriEngineering and Design

LOL!!!

You're right, Madrc570 is to blame!!!

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