Freeship KN?

I am a Naval Arch. & Marine Engr.
I am trying to use Freeship for a medium tug boat, but I feel puzzled with hydrostatics, generally the height of metacenter is termed as: KM, but I do not understand what is the meaning of KN (of course it is not Kilo Newtons).
For instnace KN.sin(phi) ?.
It is well understood that K stands for keel, but N is not to be confussed with metacenter M.

 

M is the metacentric height above the keel (K) for small heeling angles (up to 8 or 10 degrees). N is the height if the metacenter for larger angles of inclination.

To be more specific, KN sin(phi) is the horizontal distance from the keel to the center of buoyancy, or TCB.
If you subtract KG*sin(phi) from KN*sin(phi) you will end up with the righting lever GZ.

KG is sometmes called VCG.

To be exact, the exact formula for GZ is:

GZ = KN*sin(phi) - KG*sin(phi) - GG'*sin(phi) - TCG*cos(phi)

where:

KG=VCG
GG' = free surface correction for liquids
TCG = transverse location of the center of gravity

 

Martijn...Just to dumb this down a smidge for this Non engineer...but is KN sin(phi) the distance to the Transverse center of buoyancy (from the keel) for the heeled hull at B displacement and C angle of heel? Oh...and what is the value of phi?

 

Phi is the heeling angle.
KN*sin(phi) is in fact TCB.

 

Maybe this image helps.

B.t.w. remember that freeship calculates the crosscurves for a fixed trim value, which makes it pretty much to useless for small vessels.

 

So I have been ignoring it for a purpose rather than because it has been confusing me. I like that conclusion

 

Well, you can still use it as an indication of course, just don't give to much credit to the absolute values.

 

Thank you very much Mr. Martijn_vE, for your valuable information.
I will agree this is a mean to evaluate the righting arm in transversal stability calculations, but this is really the first time I found a diferent nomenclature for the Metacenter. All my books (from The University of Michigan), and SNAME booklets, all the time address the Metacenter with a "M".

 

Actually it's not that uncommon. It's just that most theory books only deal with the actual metacenter M whereas N is the "false metacenter"

See bottom left of first page: http://www.knvts.nl/S&W%20archief/Some%20stability%20issues%20of%20ships.pdf

Or some more examples:
http://books.google.nl/books?id=4E4FZ988AtYC&pg=PA176&lpg=PA176&dq=stability+ship+KN&source=bl&ots=2GnWje2HfC&sig=_vjetG12QGkVR6TWHNsQHHF1IJw&hl=nl&ei=RdPZSpiPGpTu-Ab01tS4DQ&sa=X&oi=book_result&ct=result&resnum=1&ved=0CAgQ6AEwAA#v=onepage&q=stability%20ship%20KN&f=false
http://books.google.nl/books?id=iI35oYfeCQsC&pg=PA58&lpg=PA58&dq=stability+ship+KN&source=bl&ots=FQLWeNv5Dn&sig=UTlqwnyV-BqmMyx1QhADXyWvpCc&hl=nl&ei=RdPZSpiPGpTu-Ab01tS4DQ&sa=X&oi=book_result&ct=result&resnum=4&ved=0CBsQ6AEwAw#v=onepage&q=stability%20ship%20KN&f=false

In the following book they use a strange mixture of both N and M: http://books.google.nl/books?id=iI35oYfeCQsC&pg=PA58&lpg=PA58&dq=stability+ship+KN&source=bl&ots=FQLWeNv5Dn&sig=UTlqwnyV-BqmMyx1QhADXyWvpCc&hl=nl&ei=RdPZSpiPGpTu-Ab01tS4DQ&sa=X&oi=book_result&ct=result&resnum=4&ved=0CBsQ6AEwAw#v=onepage&q=stability%20ship%20KN&f=false

I got the following image from http://en.wikipedia.org/wiki/File:GNfiguur.PNG

It indicates the difference between the Metacenter M and the "false" metacenter N, which is the intersection of KM with the centerplane.