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They also allow the designer to dimension the ship or structure so it will hold up to the most extreme sea states it will likely be subjected to based on sea state statistics. Additionally, RAOs are amplitude operators which enables to determine amplitude of motion based on a unitary wave. They are superposable, thus effective on sea state based probability solutions. Different modelling and design criteria will affect the nature of the 'ideal' RAO curves as plotted graphically being sought for a particular ship: for example, an ocean cruise liner will have a considerable emphasis placed upon minimizing accelerations to ensure the comfort of the passengers, while the stability concerns for a naval warship will be concentrated upon making the ship an effective weapons platform.
In the above, "Ship" must be interpreted widely to also include other forms of floating structures. The obvious problem in the above method is the neglection of viscous forces which contribute heavily in modes of motion like surge and roll. On a computer the above algorithm was first introduced by using strip theory and Boundary Element Method. Today both of the methods are still used if the need for fast calculations outweigh the need for precise results and the ship designer knows the limitations of strip theory.
The insight into the forces that governs the seakeeping behavior of a ship gained from the above are of course still valid within considered limits of free surface linearity. The RAO is a transfer function that is only defined when the ship motions can be assumed to be linear. The above forces can then be assembled into an equation of motion :.
It is common to only consider the absolute value of the RAO if the phase between the excitation and the ship motions are irrelevant.
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