Response Amplitude Operator

A response amplitude operator (RAO) is the transfer function that relates the amplitude of a ship motion to the amplitude of the wave that produces it, at a specific frequency, heading and speed. It is the central object of linear seakeeping analysis, because it lets the response in an irregular sea be built from the response in regular waves without simulating the irregular sea directly.

Each of the six rigid-body motions has its own RAO, and each is a function of encounter frequency rather than absolute wave frequency. Combined with a wave spectrum, an RAO gives the response spectrum, from which significant motion amplitudes, root mean square accelerations and exceedance statistics follow. The method assumes linearity, which is where it fails: parametric rolling, slamming and green water are nonlinear effects that no RAO can represent.

The full article will cover the definition and units, the computation of RAOs by strip theory and by panel methods, the phase information an RAO carries alongside amplitude, the construction of a response spectrum from a wave spectrum, model test and full-scale validation, and the specific limits that make an RAO the wrong tool for dynamic stability failure modes.