# Validating rms maxsurf and rms aqwa using manual equation

Discussion in 'Software' started by Choevlet, Aug 17, 2018.

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1. Joined: Aug 2018
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### ChoevletNew Member

I have a problem in validating the results of a ship motion from aqwa and maxsurf. When i calculated rao, the result look like same. But when i calculated rms of rolling motion. The result too much different. My assumption, i cant define how to calculate rms motion using wave frequency, spectrum, and rao. Anyone can help me? How to calculate rms of rolling motion using wave frequency, spectrum, and rao. Im using ittc spektrum. I get the value of rao from aqwa. but I can't get the rms value from the ansys aqwa program . so I have to manually define it. Thank you.

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### DolfimanSenior Member

For each degree of freedom i (= 1 to 6), the significant amplitude Xi is :
Xi = 2 * [ ∫ RAOi(ω)^2 * S(ω) * dω ]^0,5
, with
ω = wave pulsation
S(ω) = wave spectrum
RAOi (ω) = transfert functions either in motion (m/a) or in angle (°/a)

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### ChoevletNew Member

Thankyou for your reapont siir. But i want to ask.how.to get rms motion value from above formula

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### DolfimanSenior Member

rms motion value = [ ∫ RAOi(ω)^2 * S(ω) * dω ]^0,5 = [mo]^0,5
, from which, if your response spectrum follows a Rayleigh distribution ( the basic assumption), you can have :
1/3 (so-called "significant") amplitude = 2 rms
1/10 amplitude = 2,545 rms
1/100 amplitude = 3,336 rms

I prefer myself using the significant amplitude to show the response in heave, pitch or roll, .... it is more close to the crew feeling, as Hs = H1/3 is close to the usual description of a sea state.

More sophisticated computation :
To take into account the broadness of the response spectrum which could be a bit different of the narrow frequency Rayleigh distribution one, oceanographers have introduced a correction factor CF :
Significant amplitude = 2 rms CF
CF = (1-Eps^2)^0,5
Eps = (mo m4 - m2^2)/ m0 m4
mn (n=0, 2, 4) = [ ∫ RAOi(ω)^2 * ω^n * S(ω) * dω ]^0,5

All Integrales can be easily computed within an excel spreadsheet as long as you can have the RAOi(ω) and the S(ω) files

More details and explanations in this document, in particular chapter 6 Motion in an irregular sea :
Bhattacharya Dynamics of Marine Vehicles https://fr.scribd.com/doc/44416872/Bhattacharya-Dynamics-of-Marine-Vehicles

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### DolfimanSenior Member

Typo mistake for Eps, it is :
Eps^2 = (m0 m4 - m2^2 ) / m0 m4

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### Ad HocNaval Architect

Your question seems a bit muddled, unless I have misunderstood.

Are you trying to calculate the RMS of the sea spectrum, or, are you trying to calculate the mean square of the rolling amplitude?

If the later, then you'll need to take off data from the RAOs and build up a history of number of rolls and what roll angle is calculated. It is not so straight forward....just laborious.

As Dolfiman notes, this is explained in the book DMV for ease of reference.

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### Nurhalim Dwi PutraNew Member

Hello, can i ask you something? What method do you use to analyze RAO in Ansys and AQWA using the Panel Method? Can you explain to me the manual calculation step? Thank You

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