# Kn

Discussion in 'Stability' started by mermont, Oct 7, 2006.

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### mermontJunior Member

Morning
I'm an old sailor but a new boat designer(!!)
I've read some books -Dominique Presles and Pierre Gutelle(i'm french) and i have some questions about stability.
How it is possible to calculate KN for GZ calculations.I dont undesrstand the explanations of Dominique Presles in his book.

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### jehardimanSenior Member

KN? You sure you don't mean KM, the vertical distance between the keel (K) and the metacenter (M)? KM = KB+BM. KM-KG = GM, GZ = GM sin theta.

Here is a thread where I go over the entire calculation...please excuse the prissyness in the thread, I was not happy at the time with the student that asked the question.

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### jehardimanSenior Member

OK, after a couple of searches, the "KN curves" appears to be a contrivance used by IMO to calculate GZ (the righting arm) from either the cross curves of stability (mostly tankers) or just from the hull form (mostly bulkers). Note that KN curves are not the true cross curves of stability, but a short cut for mariners that allow them to calculate a specific static cross curve of stability (GZ curve) based upon an inclined KG plus a known cargo load. It is derived from the true cross curves of stability by the equation GZ = KN - KG x sin ø or KN = GZ + KG x sin ø; where GZ is first calculated in the correct method for large angles of heel for a given displacement. It can also be derived independent of true GZ. What it represents is the location on a vertical line drawn through the Center of Buoyancy (B) for a given angle of heel and displacement, that is perpendicular to the keel. See the figure on the following web page: http://www.m-i-link.com/outstation/formulaKG.asp

While this calculation is OK for wall sided, high length to beam ratios, it has a significat limitation in that it does not have a correction for either free surface changes or significant trim (bow or stern). Do a google search for "KN GZ stability".

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### RolySenior Member

Errr, Mr Hardiman sir ( hoping you don't remember my transgression)
Is there a ballpark formula, % increase in righting moment, if you increase the deadwood of a sailboat by a finite amount, but keep everything else the same. (lead bulb keel)
Guess I really deserve to be ignored.

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### PNACSNaval Architect

KN Curve & GZ Curve are different representations of righting arm. GZ is the righting arm with respect to Vertical Center of Gravity (VCG), where as KN is the righting arm with respect to Keel (or VCG = 0).KN Curve is constant for a vessel at a particular displacement, while GZ curve will be vary depending on the VCG (or loading conditions) for same draft. Once the KN curve is derived for a particular draft, GZ can be easily calculated for any loading condition (any VCG) using the formula GZ = KN - VCG*Sin(heel). That’s the significance of KN Curve.

Calculation of KN or GZ curve is a lengthy process & everyone is using software now a days. But the basic principles can be understood from the books you are reading now.

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### PNACSNaval Architect

Roly,

There is no linear relation between them.

if you can calculate reduction in VCG of your sail boat after addition of deadwood, new GZ curve can be fairly obtained as follows.

new righting arm value for a heel (G'Z') = present GZ + GG'*Sin(heel)

Here i ignored the change in draft of vessel due to deadwood, for simplicity

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### RolySenior Member

Phew.....thanks Pnacs.
If it is even a little less tender, I will be happy.

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