Q&A forum: RAO calculator for floating vessels
(response amplitude operators)

There is no such thing as accuracy in vessel motion calculations. Sea-states are based upon statistics, which is nothing more than an educated guess.
Because a vessel never finishes its motion cycle with any wave in any sea-state, its orientation at the start of a cycle is impossible to define.
Mathematicians have developed many vessel motion theories over the years, some will work better for particular vessel properties and a given 'sea-state' than others, but that doesn't make it more (or less) accurate.
ANSYS applies one theory and we apply another, whilst they are both valid, they will work differently for different waves/sea-states.
Because of this unreliability of sea-state statistics, CalQlata's vessel motions (RAO) calculator calculates for a single wave, it does not apply sea-states.

The displacement in the default calculation must be kilograms because the water density is in kilograms (per cubic metre).
However, you may change the units to whatever you prefer, but you must be consistent. If, for example, you prefer tonnes, the water density should be entered in tonnes (per cubic metre).

... make sure that the decimal is a ‘point’ not a ‘comma’ in your computer language?
and
You will see in image-1 (attached) that the input data in RAO and Vessac are compatible.
In the image-2 (attached) the RAO input data has been modified. The calculation is saved (into its Data file), and Vessac then uploads from the RAO data file.
If you haven't saved the RAO calculation to disk, Vessac will simply load the old data.

Should a customer that has previously purchased a copy of this calculator, like a copy of the revised version, please get in touch by email and a copy will be sent free of charge.

Thank you for the detailed spreadsheet. It is very helpful. I have taken the input and output data and compared them with my own comparative calculation in the attached spreadsheet. The only two differences are for roll and pitch, which I can explain as follows:
Roll and Pitch are normally calculated without the inclusion of the following particular dynamic amplification factor;
γ(Ω,ξ) = 1 / √[(1 - Ω²)² + 4 * (Ratio * Ω)²]
which was the procedure I adopted in my first calculator. However, I have always felt a little uneasy about ignoring the above factor despite it being general practice.
So I have included it in my latest calculator and roll and pitch are now modified thus;
roll or pitch = (γ(Ω,ξ) * α) * Cos(ωe * pₑ * θ / 2π - Φ)
Therefore, you should expect that Rᴿᴬ (roll) & Pᴿᴬ (pitch) will be different between the new calculator and the earlier version. I would normally (but not necessarily) expect the new calculator to predict higher roll and pitch RAs than before.

It is important to understand that vessel response amplitudes are not an exact science. Various theories have been established according to personal preferences.
None of them are correct. They are simply a means of anticipating vessel response due to mass displacement.
Some theories appear a better fit with particular vessels and seastates than others.
Given that no two following waves are the same, RA & RAO theories can never be better than a calculated guestimate.
Personally, I feel happier with my latest approach. But beware of reading too much accuracy into the results. Like vortex shedding, if you get too close to a vessel's natural frequency, RA and RAO calculations will become meaningless.