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

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Trying to use Vessacc and RAO we found that applying the DVN rules was giving lower results than the harmonic for small waves.

We bought another version through one of my young engineers (Vasilis Papadopoulos) and then we found that there was a problem in the previous editions of Vessacc and RAO which I got.

We check also the waves but we found no problem between the 2 editions.

I am sending you, for your consideration, the slides with the comparison, together with the excel file of the data. The results are for a specific angle μ (angle of wave direction in respect to vessel direction), and a specific angle θ (angle through the wave). For different angles you get bigger or smaller x,y,z components for acceleration.

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.

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