GZ curve

[jimmymc90]

I am trying to produce a GZ curve after a redesign of a Ferry. The problem is I dont have the KN values from the Hydrostatic Data for each heeling angle. Is there an easy way for me to calculate these KN values so I can work out the righting arm for each heeling angle.

thanks,
James

[jehardiman]

Why don't you calculate the GZ directly? The "KN curves" are 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".

[jimmymc90]

Thanks a lot for your advice jehardiman, I actual spoke to a Naval Architect today about this and he told me that without knowing the KN values I would not be able to produce a GZ curve. He told me that these are only found by using a complex computer algorithm but I guess he was wrong.

james

[jehardiman]

Realisticly, he is kind of right. The KN vs heel curve is identical to the GZ vs heel curve if you set KG == 0. You still need to have or work up a set of Displacement & Other (D&O) curves. This can be simple, complex, or just plain tedious depending what data you have and what form it is in. If you have a body plan and a scaled acetate doily it is about an hours work with a spreadsheet and proportional dividers (there...I showed my age...too many people think some things can only be done by computer but have forgotten when we did it by hand).