The friction, eddy, and appendage induced roll damping components are nonlinear and could be assumed to be proportional to the square of roll angular velocity, which is expressed as the quadratic:

(7–14)

in the local structure axes (LSA), where is the roll angular velocity at time and is the quadratic roll damping coefficient which can be derived from experiemental data or given by any empirical formula other than the forms discussed in Nonlinear Bilge Vortex Shedding Damping and Bilge Keel Damping.