RAO (Response Amplitude Operator)

A response amplitude operator (RAO) is the linear transfer function giving the amplitude (and phase) of a ship motion per unit wave amplitude as a function of wave frequency and heading. Computed from strip theory or 3D panel methods, RAOs are squared and multiplied by the wave energy spectrum, then integrated, to predict the variance of each motion in an irregular seaway. They are the core of frequency-domain seakeeping and operability assessment.