Superyacht - - Tecnica -

When you fill a pool aboard a ves­sel it loo­ses sta­bi­li­ty for two rea­sons: The con­si­de­ra­ble weight (the wa­ter in the pool) that’s mo­ved from the tanks, usual­ly pla­ced low do­wn, to the pool that’s ge­ne­ral­ly qui­te hi­gh up, usual­ly on an open deck. The oscil­la­tion of the sur­fa­ce wa­ter in the pool (free sur­fa­ce ef­fect). If the fir­st cau­se of sta­bi­li­ty is so­mewhat ob­vious (the ship’s cen­tre of gra­vi­ty ri­ses as a func­tion of the amount of wa­ter mo­ved and the di­stan­ce it’s rai­sed up), the se­cond cau­se is a bit less in­tui­ti­ve. So let’s get to grips wi­th it. A li­quid load aboard, if its not kept in a sea­led tank, will be free to mo­ve in its con­tai­ner and chan­ge the sha­pe of its vo­lu­me. In par­ti­cu­lar it’ll be the sur­fa­ce of this li­quid load that’ll chan­ge sha­pe: the so-cal­led “free sur­fa­ce ef­fect “. A pool on board is a “free sur­fa­ce”.the me­re pre­sen­ce of this li­quid sur­fa­ce, in other words of a wa­te­ry mass free to oscil­la­te, cau­ses a re­duc­tion in a ves­sel’s sta­bi­li­ty, in that the me­ta­cen­tric ra­dius of the hull “r” is re­du­ced, and con­se­quen­tly al­so the me­ta­cen­tric height “r-a”. In the ca­se of a pool, whe­re the wa­ter con­tai­ned in the tank is ma­de up of wa­ter of a den­si­ty si­mi­lar to that of the sea­wa­ter in whi­ch the ves­sel is sai­ling, the re­du­ced me­ta­cen­tric height de­pends so­le­ly on the geo­me­try of the li­quid sur­fa­ce, or, to be mo­re pre­ci­se, on the mo­ment of iner­tia “i” of the li­quid sur­fa­ce wi­th re­spect to the ba­ry­cen­tric axis pa­ral­lel to the sym­me­tric lon­gi­tu­di­nal pla­ne of the ves­sel. In ef­fect if a ves­sel’s righting mo­ment, that is the abi­li­ty of the ves­sel to re­turn to its ho­ri­zon­tal po­si­tion af­ter ha­ving li­sted due to an ex­ter­nal cau­se (wind, wa­ves or wha­te­ver), is gi­ven by the fol­lo­wing re­la­tion (for small in­cli­na­tions wi­thin the li­mi­ts of the me­ta­me­tric me­thod): RM = D (r-a) si­ne a then the pre­sen­ce of a li­quid sur­fa­ce (in this ca­se of wa­ter) free to oscil­la­te re­du­ces righting mo­ment as fol­lo­ws: RM = D (r-a) si­ne a - (p i/v) si­ne a As the event be­co­mes re­pe­ti­ti­ve the re­la­tion sim­pli­fies and be­co­mes: RM = D (r-a-i/v) si­ne a Whe­re RM = Right Mo­ment (r-a) = me­ta­cen­tric height a = an­gle of li­st p = weight of li­quid i = mo­ment of iner­tia of the sur­fa­ce of the pool v = vo­lu­me of li­quid V = vo­lu­me of ves­sel’s hull

In ef­fect the righting mo­tion fac­tor RM re­du­ces as a func­tion of the mo­ment of iner­tia of the sur­fa­ce wa­ter in the pool, a mo­ment of iner­tia that re­pre­sen­ts the re­si­stan­ce (iner­tia in­deed) again­st chan­ging its sha­pe for a sim­ple sha­pe su­ch as

the one for a rec­tan­gu­lar pool, said mo­ment of iner­tia will be gi­ven by: i = (L * B3)/12 whe­re L is the leng­th and B the wid­th of the pool that is ele­va­ted to the po­wer of 3. The cor­re­la­tion thus tells us that the re­duc­tion in sta­bi­li­ty is so­le­ly a func­tion of the si­ze of the sur­fa­ce of the pool, in other words its mo­ment of iner­tia, and not of the amount of wa­ter held in the pool. It is thus evi­dent that the wi­der the pool the less sta­ble a ves­sel will be. This is why tanks on board, at lea­st the lar­ger ones, al­ways ha­ve baf­fles that split them up in­to com­part­men­ts so as to li­mit L e B and, thus, re­du­ce mo­ment of iner­tia. The sa­me ex­pe­dient is used on tan­kers. To gi­ve an idea of how dan­ge­rous an open sur­fa­ce of wa­ter can be on board, for­get­ting for a mo­ment pools and tanks, it is enou­gh to re­mem­ber the dan­ger re­pre­sen­ted by a deck floo­ded wi­th sea­wa­ter or rain, should it be im­pos­si­ble to di­schar­ge the wa­ter quic­kly; this is a gra­ve dan­ger for ves­sels, even when the quan­ti­ty of wa­ter is mi­ni­mal.

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