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. More advanced programs that are used today utilizes Boundary Element Method through different applications (such as WAMIT, SESAM WADAM, MOSES, NeMOH and ANSYS AQWA) some may also include the effects of viscosity. 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 Orcina convention is to use the amplitude of response (in length units for surge, sway, heave, in degrees for roll, pitch, yaw) per unit wave amplitude, and to use the phase lag from the time the wave crest passes the RAO origin until the maximum positive excursion is reached (in other words, the phase origin being at the RAO origin). Mathematically, this is given by

The vessel has 6 degrees of freedom: 3 translations (surge, sway, heave) and 3 rotations (roll, pitch, yaw), so the RAO data consist of 6 amplitude and phase pairs for each wave period and direction. The RAO amplitude and phase vary for different types of vessel, and for a given vessel type they vary with draught, wave direction, forward speed and wave period / frequency. It is important to obtain accurate values for the RAO amplitude and phase if the dynamics of the system are to be correctly modelled. Where x {\displaystyle x} is a rigid body motion such as heave, ω {\displaystyle \omega } is the oscillation frequency, M {\displaystyle M} is the structural mass and inertia A ( ω ) {\displaystyle A(\omega )} is the added mass (frequency dependent), B ( ω ) {\displaystyle B(\omega )} is the linear damping (frequency dependent), C {\displaystyle C} is the restoring force coefficient (stiffness matrix) and F ( ω ) {\displaystyle F(\omega )} is the harmonic excitation force proportional to the incoming wave ζ = ζ a e i ω t {\displaystyle \zeta =\zeta _{a}eA surge RAO of 0.5 in a wave of height 4m (and hence wave amplitude 2m) means that the vessel surges to and fro -1m to +1m from its static position; a pitch RAO of 0.5° per metre in the same wave means that the vessel pitches from -1° to + 1°. The coordinate system used to define vessel motions and, in particular, which direction is positive. That is, whether surge is positive forward or aft, whether heave is positive up or down and whether pitch is positive bow up or bow down. Frank looked around the room. "That first table there, they gave their table to this group at the bar. These guys are all executives from PepsiCo. If you have a table, you can give it to your friends, your business associates, or to a charity auction. I had Bobby Flay, Michael Romano, a whole bunch of big chefs last week and I didn' t know they're coming. I never know who's coming in. That's what makes it wonderful. It's serendipity. There's no grand design or plan. The only caveat is if you're not going to use your table and no one else is going to use that table, that's when you call me."

A waiter comes over and says he's setting a table for us. We invite Frank to join us, since it's unclear whether he's eaten tonight, but he politely declines. He says he'll come sit with us later on, but he won't eat.Anthony! This is Anthony Abbot," Frank says. "He's a member of Stanwich, a great golf club. He invites me to play golf with him." Abbot went on a golf trip with 11 other guys 20 years ago. Frank was one of them, and when names were drawn out of a hat, he and Abbot were matched up.