For the irregular wave case, to minimize the least squares error of energy dissipation, the equivalent linear roll damping with respect to the local roll axis is:

(12–17)

where is the RMS of roll angular velocity and is the quadratic roll damping coefficient defined in either Equation 7–13 or Equation 7–14.

When the bilge vortex shedding roll drag is included, the Keulegan-Carpenter number for bilge is amended from Equation 7–4 as:

(12–18)