Vessel types: How to check RAOs

For each draught and wave direction, you should check that the curves on the complex value RAO graphs are reasonably smooth and approach the circle, which is the expected long-wave limit for a free-floating vessel. Note that:

• The curve might not approach the expected long-wave limit if the RAO data do not include values for any long waves. Wave periods over 20 seconds for ships, or 30 seconds for semisubmersibles, are considered to be sufficiently long for this purpose.
• The curve might also not approach the circle if the vessel is not free-floating. For example the heave displacement RAO amplitude of a tension leg platform will not approach the usual long-wave limit of 1.
• The circle on the yaw graph only applies to slender vessels (i.e. long in the $x$-direction and narrow in the $y$-direction).
• Smooth graphs can only be expected if the data includes RAOs for reasonably closely spaced periods.

As examples, consider the following three graphs:

The first shows a typical, well-behaved set of displacement RAO data – the curve is smooth and the long-wave limit agrees with the expected value marked by the circle.

For a freely floating vessel, the second graph is clearly in error, since the curve does not lead to the expected long-wave limit. The RAO data for long waves (represented by the end of the curve) has the correct amplitude, but its phase differs by 180° from the expected long-wave value (represented by the circle). There are two likely causes – it may be that the phase lead/lag convention has been set wrongly (this would give a phase angle sign error), or that the convention for the direction of positive motion has been set wrongly (this would give a phase error of 180°).

The curve on the third graph approaches the expected long-wave limit, but then suddenly goes to zero. This suggests that the RAO data for infinite period has not been set correctly.

Common problems

It is not unusual to be given RAO data for a vessel but not be given all the conventions that apply to the data. Below are some common problems and their symptoms. But beware that several common problems have very similar symptoms, so it is not always possible to identify the problem. It is therefore important to get as much information as possible from the original RAO data supplier.

• The quoted wave direction might be measured clockwise (viewed from above) from the $x$-direction, rather than anticlockwise (the OrcaFlex convention). The effect would be a 180° shift in the sway, roll and yaw phases.
• The quoted wave direction may be the direction the wave is coming from, rather than the direction it is progressing towards (the OrcaFlex convention). The effect would be to negate all the phase values.
• The phases may be leads instead of lags. OrcaFlex will accept either as specified by the RAO phase conventions. The effect of an error here would be to negate all the phase values.