## Vessel types: Checking RAOs |

The **check RAOs** button on the vessel types form allows a visual check on the RAO data for either displacement RAOs or wave load RAOs. For a given draught and wave direction, it displays graphs (one for each vessel degree of freedom) showing how the RAO and phase vary with wave period.

There are 3 types of graph available:

- complex value
- amplitude
- phase

The graphs initially show the RAOs for the currently selected draught and direction. You can switch to other draughts and directions, either by using the navigation buttons at the bottom of the form to step through the data or by selecting from the drop-down lists. You can change the scale of the graphs (double click on the graph and change the ranges of the axes).

These graphs provide a straightforward graphical representation of the RAO data as input on the vessel types data form for the given RAO origin. The amplitude or phase is represented on the $Y$ axis of the graph; on the $X$ axis you may choose period, frequency in rad/s or frequency in Hz.

The graphs represents RAOs as points in polar coordinates $(R,\phi)$, where

- $R$ is the non-dimensional amplitude
- $\phi$ is the phase
*lead*, from the time the wave crest passes the phase origin until the maximum positive motion occurs.

Figure: | Complex value RAO graph |

The graph depicts the RAO data for the given RAO origin, and has two parts:

- A curve showing the user data as a series of points joined in order of increasing period. The curve starts from the short-wave response, which should have zero or very small amplitude, so the curve should begin near the origin. Moving along the curve away from the origin corresponds to the wave period increasing from zero. For surge, sway and heave, the other end of the curve is the long-wave response for the longest period given (which may be infinite). For roll, pitch and yaw, the point on the curve for infinite period cannot be calculated, so instead we end their curves with the RAO data for the largest
*finite*period given. - A solid circle representing the expected long-wave response limit for a freely floating vessel.

Warning: | The expected long-wave response limits calculated by OrcaFlex only apply to free-floating vessels. Also, the yaw response limit only applies to slender vessels that are long in their $x$-direction and narrow in their $y$-direction. |

The purpose of the complex-value graph is help you check your RAO data – the curve should normally be reasonably smooth and tend towards the expected limit shown by the solid circle.

For displacement RAOs, the non-dimensional values $R$ for surge, sway and heave are the vessel translation amplitudes divided by the wave amplitude. For roll, pitch and yaw displacement RAOs, $R$ is the rotational response normalised with respect to maximum wave slope – i.e. it is vessel rotation amplitude divided by the maximum wave slope.

For wave load RAOs, $R$ is found for both translation and rotation by normalising both the forces and moments applied to the vessel using wave amplitude.

Note: | The complex-value graphs are drawn using the standard OrcaFlex conventions: positive surge is forward, positive sway is to port, positive heave is up, positive roll is starboard down, positive pitch is bow down and positive yaw is bow to port. These are not necessarily the same as the chosen vessel type RAO conventions. |

This polar coordinates way of representing RAOs is rather more helpful than drawing separate graphs of amplitude and phase, since it presents all the information on a single graph and also the resulting curves are smooth, whereas phase graphs frequently show phase jumps.