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: In the field of ship design and design of other floating structures, a response amplitude operator ( RAO) is an engineering statistic, or set of such statistics, that are used to determine the likely behavior of a ship when operating at sea. Known by the acronym of RAO, response amplitude operators are usually obtained from models of proposed ship designs tested in a model basin, or from running specialized CFD computer programs, often both. RAOs are usually calculated for all ship motions and for all wave headings. The system used to define wave direction. In OrcaFlex 0° means waves approaching the vessel from astern and 90° means waves coming from the starboard side, but if a different convention applies to your data then you must allow for this when entering the data. Just think about what happened while you were here," he tells me, putting his hand on my forearm for emphasis. "You met my tailor. You met Tony Tantillo. You met Tony Abbot." (I met a trio of Tonys, if you include Tony the bartender.) "You met all these people. You met the congressman. You're seeing Rao's." And because it's so bright, which Frank says is because "it adds to the energy of the room," I really am seeing everything.

And this is Tony Tantillo. He's on CBS every day, cooking with his daughter," Frank says, introducing us to another friend who's come up to the bar. "Listen, Tantillo. I gotta tell you. You're too good-looking. You're too handsome." 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. Can't hear you," he says, pointing to his ear. (Now I understand whom the gruff waiters at Carbone are copying.) As it turns out, Frank sang in a group called the Holidaes in the 1960s. "I was an old doo-wop guy," he says. "I get Billy Joel, Sting, Jimmy Fallon in here. Jimmy Fallon loves to sing doo-wops! So whenever he's here, I start singing, and boom, he jumps up and starts singing. And before you know it the whole room is going nuts."The Diffraction forces, which are pressures that occur due to the disturbances in the water because of a body being present. RAOs can be obtained either from model tests or from diffraction analysis software. The data may be presented in tabular or graphical form: tables of numbers are better for our purposes since they can be imported directly into OrcaFlex (see importing hydrodynamic data).

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 reference time for phase angles, and the reporting convention used (e.g. whether phases are reported as lags or leads). Again, OrcaFlex allows a range of options.

And you would be protected," he tells her. "I am a gentleman and I only allow gentlemen. If anybody is stupid, I would be right there. I only allow ladies and gentlemen. I don't want anything else." 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." In the old days, Abbot says, Frank used to open the reservation book on a quarterly basis and when he came by to get his table assignment, Donald Trump was waiting in line outside the door with other regulars. RAOs are effectively transfer functions used to determine the effect that a sea state will have upon the motion of a ship through the water, and therefore, for example, whether or not (in the case of cargo vessels) the addition of cargo to the vessel will require measures to be taken to improve stability and prevent the cargo from shifting within the vessel. Generation of extensive RAOs at the design phase allows shipbuilders to determine the modifications to a design that may be required for safety reasons (i.e., to make the design robust and resistant to capsizing or sinking in highly adverse sea conditions) or to improve performance (e.g., improve top speed, fuel consumption, stability in rough seas). RAOs are computed in tandem with the generation of a hydrodynamic database, which is a model of the effects of water pressure upon the ship's hull under a wide variety of flow conditions. Together, the RAOs and hydrodynamic database provide (inasmuch as this is possible within modelling and engineering constraints) certain assurances about the behavior of a proposed ship design. 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). 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.