Gyradius

The gyradius, or radius of gyration k, is the distance from a reference axis at which the whole mass could be concentrated to give the same mass moment of inertia, defined by I = m times k squared. For ship motions the pitch gyradius k_yy is typically 0.24 to 0.26 times the length L, the roll gyradius k_xx about 0.30 to 0.40 times the beam B, and yaw k_zz close to k_yy. These ratios set the dry moments of inertia in the pitch, roll, and yaw equations and therefore the natural periods, so loading-condition weight distribution that changes k directly shifts the roll and pitch resonant periods.