# Vessel types: RAOs

OrcaFlex uses two different types of RAO (response amplitude operator): Displacement RAOs and wave load RAOs.

Displacement RAOs are specified on the displacement RAOs page on the vessel type data form. They define the 1st order motion of the vessel in response to waves of given period and amplitude. They are only applied if the vessel superimposed motion is set to RAOs + harmonics (but note that they are also required if QTF modifications are being applied). In the dynamic analysis the vessel moves harmonically, in all 6 degrees of freedom, about its primary position. These harmonic motions are specified by giving the RAO amplitudes and phases, for all six degrees of freedom, usually for a range of wave periods and directions.

Wave load RAOs are specified on the load RAOs page on the vessel type data form. They define the 1st order wave force and moment on the vessel due to waves of given period and amplitude. They are only used if the 1st order wave loads are included for the vessel and they only affect the motion if the vessel primary motion is set to one of the calculated options.

The two types of RAOs are specified in very similar ways, using the following data. And for both there is a check RAOs button that provides RAO graphs that help detect errors.

### RAO origin

The RAO origin is the point on the vessel whose motion is defined by the RAOs. The RAO origin is specified by giving its coordinates with respect to the OrcaFlex vessel axes (not the directions specified on the conventions page). It is commonly, but does not need to be, at the centre of mass. Different draughts can use different RAO origins.

### RAO phase origin

The RAO phase origin is the point on the vessel to which the RAO phase values are relative. It is specified by giving its coordinates with respect to the OrcaFlex vessel axes (not the directions specified on the conventions page). The phase values given in the RAOs must be relative to the time that a particular point on the wave (crest / trough / zero up- or down-crossing, depending on the RAO phase conventions) passes the specified RAO phase origin.

Often the phase origin is the same as the RAO origin, i.e. the phases are relative to the time the crest or trough passes the point whose motion the RAOs define. In this case the phase origin can be set to '~', meaning 'same as RAO origin'. But note that some programs (one example being MOSES) generate RAOs where the phase origin is not necessarily the same as the RAO origin.

### RAO data

RAO data can be specified for a number of different wave directions relative to the vessel, using the OrcaFlex direction convention. This relative wave direction is the direction in which the wave is progressing, measured positive from the vessel x-direction towards the vessel y-direction, and on the RAOs page of the vessel type data form each RAO table is labelled with its associated direction.

To change the value of the wave direction for one of the RAO tables, select the tab for that table and edit the selected direction. To insert a new wave direction after an existing direction, select the existing direction's page and click the insert direction button. Similarly, the delete direction button deletes the currently selected direction.

For each direction, the RAO table covers a range of wave periods or frequencies, as specified in the conventions data. The periods/frequencies need not be entered in order – OrcaFlex will sort the table before use.

In the case of a circular symmetric vessel, RAOs are specified for only one wave direction – OrcaFlex will derive RAOs for all other directions.

## RAO interpolation/extrapolation

### On direction

You must provide RAO tables that include or span the wave direction(s) involved in the simulation. If RAOs are required for a wave direction, relative to the vessel heading (primary heading for displacement RAOs, diffraction frame heading for wave load RAOs) for which an RAO table has not been supplied, then OrcaFlex will use linear interpolation to obtain an RAO table for that direction.

 Warning: Interpolation is likely to be poor if the interval involved is large. We therefore recommend that the RAO directions defined cover all the wave directions that will be used in steps of 30° or less.

### On period

For regular wave analysis, RAO data are only needed for the appropriate wave period, or for wave periods either side of that period. For random sea simulations, RAO data should be specified for a wide enough range of wave periods to cover the spectrum. The view wave components button (on the waves page of the environment data form) reports the wave frequencies that OrcaFlex will use to represent the spectrum.

 Note: If the vessel length differs from the vessel type length then the RAO periods given on the vessel type form are Froude scaled, and it is these Froude scaled periods that must cover the actual wave period(s).

Linear interpolation is used if RAOs are required for a period that is between the periods given in the table. For periods shorter than the smallest value in the table, OrcaFlex will assume a zero amplitude response at zero period and apply linear interpolation between that and the shortest period value. If you specify an RAO for zero period which has non-zero response, OrcaFlex will override this with a zero response, since a non-zero response at zero period is physically implausible. In both of these cases, OrcaFlex will issue a warning. To avoid this warning, simply define a zero-amplitude response at zero period in your RAO tables.

For periods longer than the longest period specified in the table, OrcaFlex will use the RAOs given for that longest period. You will be warned if there are wave components in the sea state that will be affected by this. To avoid this warning, you may define the RAO for period=infinity, which for a free-floating vessel can be derived from the knowledge that the vessel must follow the surface in a sufficiently long wave. See RAO quality checks for details.

### Complex-valued interpolation

Note that RAO interpolation is done using the complex-value representation of the RAOs, in which the RAO with amplitude $a$ and phase lag $\phi$ is represented by the complex number $$C(a,\phi) = a\,e^{-i\phi}$$ For example, given RAOs $(a_1,\phi_1)$ for direction $\beta_1$ and $(a_2,\phi_2)$ for direction $\beta_2$, the interpolated RAO for the intermediate direction $\beta = \frac12(\beta_1+\beta_2)$ is $(a,\phi)$, where $$C(a,\phi) = \tfrac12\left[C(a_1,\phi_1) + C(a_2,\phi_2)\right]$$ This gives better results than interpolating the amplitude and phase separately.

OrcaFlex first interpolates on period, to obtain RAO tables whose entries correspond to the wave component periods. It then interpolates these tables on direction relative to the vessel (which will be changing during the simulation if the vessel heading changes) to obtain the RAOs for the appropriate wave periods and directions. Both of these stages are done using complex-valued interpolation.

## Obtaining the data

All of the above RAO data can generally be obtained from the results of a diffraction program. OrcaFlex can import these data, and much else, directly from the output files of some specific programs (AQWA and WAMIT) and from generic text files with OrcaFlex-specific markers added.