Cross-curves of stability (KN curves)

Cross-curves of stability, or KN curves, plot the righting arm referenced to the keel, KN, against displacement for a set of fixed heel angles (commonly 10, 20, 30, 40, 50, 60, 75 degrees). They are a hull property, computed for an assumed G at the keel, so they are independent of the actual loading. To get the real righting arm at a given condition, the user reads KN at the operating displacement and corrects for the true KG: GZ = KN minus KG * sin(theta). This converts hull geometry into the GZ curve checked against the IMO 2008 IS Code. Free-trim cross-curves let the ship trim freely at each heel angle.