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I am that old! I could be your father!" says Frank, who will celebrate his 70th birthday this year. As well as displacement RAOs, which directly specify the motion of a vessel in waves, OrcaFlex can apply wave load RAOs, which represent instead the load (force and moment) on a vessel due to waves. In this case, the amplitude represents the magnitude of the force (in the surge, sway or heave direction) or moment (in the roll, pitch or yaw direction); the meaning of the phase remains unchanged. Example: Finding the forces on the ship when it is restrained from motion and subjected to regular waves. The forces acting on the body are:
The first thing I noticed when we walked in was how bright the place is. It may be the brightest fine-dining establishment I've ever been to. The second thing I noticed was all the Christmas decorations (a story I'd read said they stay up year-round). Every chair at every table was full and the bar was crowded. An older bespectacled man sat on a stool in the corner, surveying the room, and motioned to suggest we sit at the two stools open next to him. A 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°. One deuce," Emma—who's in graduate school and until recently worked part-time as a restaurant hostess—corrects me.
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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 Damping (Hydrodynamic) forces due to the oscillations creating outgoing waves which carry energy away from the ship.
There are many different conventions for defining RAOs. There have been attempts at standardisation, but these have not been successful so there remain differences between the main computer programs and model basins: some establishments even use different conventions for reporting model and computed data. The only safe course is to obtain a complete description of the system used for the data in each case. 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. No one gives them up," he says. "Every table has been booked every night for the past 38 years. There's weeklies, biweeklies, monthlies, and quarterlies, so in every three-month period, I see all my clients. And now I'm dealing with their children and grandchildren."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}e 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. Whose table are you at?" he asked. I said we weren't at a table and had stopped in for a drink. (The tables, as I knew, are all "owned" by regulars who come themselves, invite friends, or donate the table to charity auctions where just the reservation regularly sells for thousands). 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."
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. 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 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. Finding the forces on the ship when it is forced to oscillate in still water conditions. The forces are divided into: 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.
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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. 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. Although OrcaFlex allows the RAO input data to use a wide range of systems, all OrcaFlex results use a right-handed system in which the positive movements are as follows: Surge
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