# stability calculation formula

Discussion in 'Stability' started by hbr, Dec 29, 2007.

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### hbrJunior Member

All,

A text book with title "naval architect" provides me for stability with following formula for a sailing yacht:
Mr = 400.B^3.L.sin(teta-0,0022.teta^2)+9.81.(k1.Q-k2.C-k3.G).sin teta+500.B

without any other further explanation,
Q is the mass of the keel,
G is the mass of the mast/sail/
C is the mass of the hull (total hull with underwater part included)

the second term corresponds with the moments of weight,

can somebody explain me these 2 other different terms that are used to calculate the specific moment ?

Best Regards,

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### GuillermoIngeniero Naval

Hi, hbr.
I didn't know that formula. Can you please post more details on the book?
Also: where from do you get the values for k1, k2 and k3?

B^3 * L seems to me a moment of inertia related with floatation area (B and L are at the WL?)
500 B seems to be just an adjusting term.

Cheers.

Last edited: Jan 5, 2008
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### hbrJunior Member

book reference

Guilermo,

it is a book in French language,
title : Architecture Navale connaissance et pratique
written by D. Presles & D. Paulet.

in the second part an example for a sailing boat is included,
the example provides the formula that was posted,
trying to understand the method or principle that is applicable for the proposed calculation.

Any suggestion is appreciated.

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### AlikSenior Member

My feeling is that very structure of this formula is wrong.
It should be: RM=GZ*DISPL or RM=GM*sin(Teta)*DISPL for small angles of heel

where RM - rigthing moment (suppose same with Mr in formula); DISPL - displacement; GZ in GM - traditional righting arm and metacentric height, Teta - heel angle.

In this formula I can see DISPL in second item, but it is missing in first and third. I would suggest that even simplified formulas should have physical sence, otherwise it is too risky to use it.

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### AlikSenior Member

Few years ago we have proposed simplified method to estimate stability curve for sailing boat. It works for LWL/BWL=2...5; BWL/Tc=2...8; H/Tc=1...6 where H is hull depth excluding cabin.

GZ30=0.44*GM
GZ60=0.325*BWL+0.250*H-0.268*Tc-0.866*VCG
GZ90=0.54*H-VCG

VCG is measured from bottom of boat. GM and VCG are supposed to derive from inclination test.
Published here: Nazarov A., Nazarova L. Sailcraft stability analysis from experimental results // Proceedings of Sevastopol Nakhimov Nautical Institute, Sevastopol, 2003, Vol.3 –. p.132-135. (in Russian)

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### hbrJunior Member

Alik,

posted the question since i could not find any reference at all.

BR

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### hbrJunior Member

Alik,

Was the proposed formula accepted/validated ?

Is there a certain side effect to be expected due to the simplification ?

BR
Hugo

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### AlikSenior Member

These are not official formulas. We have developed systematic series of 3D hull shapes and run them through stability software. We have validated it for few boats since then. Yes, superstructure shape and transom width can effect the accuracy, but these formulas provide error to safe side. These formulas are intended for getting safety assesment based on inclination tests results (or measurement certificate), if stability curve is missing.

P.S. The formula for 90 degrees derives from IOR.

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### hbrJunior Member

Alik,

Thanks a lot for your contribution,
appreciated,

Hugo

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### ImanNew Member

Simplified formula of GM

Hi,
I need an emprical(simplified) formula of GM.
I'd be grateful if you help me.
Thanks
Iman

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### GuillermoIngeniero Naval

GM = (f *B/t)^2

Being "B" the breadth in meters, "t" the rolling period in seconds in calm waters, which can be easily obtained from a roll decay test, and "f" a factor depending on the type of vessel and load condition.

More at: http://www.tc.gc.ca/eng/marinesafety/tp-tp2534-appendix-iii-1543.htm

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