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AbstractThis paper reports seakeeping studies performed on a parametrically varied set of SWATHhull forms. The SWATH form, because of its de-linked nature of design affords many vari-ations of the underwater hull geometry without affecting overall deck length and beam. Fora given displacement, the hull form can be varied in terms of length, basic section shape,maximum area of cross section of under water hull and strut water plane shape. Using thesevariants, a parametric family of hull forms has been generated employing Chebychev poly-nomial scheme for representing sectional area distribution and using a bi-quintic B-spline basedsurface definition scheme. Not all designs offer optimal performance in a given sea state. Atwin-hull motion analysis program SEDOS has been used to study the motions and otherdynamic effects. Setting criteria for operability, these dynamic effects have been quantifiedinto a single value namely, operability index. The approach here fulfils an investigation at thedesign stage in order to tap the full advantage of the SWATH form. 58415
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The study brings out amethodology for assessment of the SWATH at the design stage highlighting interesting resultsrelated to section shapes and sectional area distribution. Thus, combining a newly developedinteractive surface generation scheme with an analysis package, a rapid assessment tool isoffered for new design. 2002 Published by Elsevier Science Ltd. 1. IntroductionDuring the past decades, seakeeping has come to be understood as a complexcombination of characteristics that determine ship behaviour in waves. Estimationof seaworthiness of ships at an early design stage is of great importance in selectinga seaworthy hull form, from among those that meet other design requirements. Theability to readily analyze the relationship between hull form modifications and sea-worthiness can allow consideration of many hull forms in a short period of time.Seakeeping performance index is a term used to assess the motion and dynamiceffects for a given sea state, direction of heading angle and speed of transit. Sincesea state and heading angle are probabilistic in nature and speed of transit may varyaccording to mission requirements, the effects of all these factors must be combinedinto an overall performance index. Thus a seakeeping performance index is evolvednot just based on the hull form and geometry but also based on the above operationaland external characteristics. SWATH ships, by the nature of their special geometricform, must be specifically assessed for performance index with due consideration fordefining their limiting operating conditions. A hull form with favourable behaviour inone sea-state may not necessarily behave favourably in another. Also not all designsoffer optimal performance in a given sea state. For this purpose, keeping displace-ment constant, the hull forms have been evolved using a convergent Chebychevscheme for representation of sectional areas distribution as well as strut thickness dis-tribution.A family of forms with parametric variants has been assessed for seaworthinesscharacteristics. The common feature of a family is constant displacement and thevariants introduced within a family are change in cross section shape, length, anddistribution of area of cross section.2. Contemporary methods of assessment of performanceBlok and Beukelman (1984) compared hull forms on their seakeeping merits usinga regression predictor model based on number of hull shapes, by arriving at onesingle figure of merit for heave, pitch and acceleration. McCreight (1987) used meas-ures of merit for assessing seaworthiness namely Limited Significant Wave Height(LSWH) and percentage time of operation (PTO) during which the vessel performswithout degradation of operation.
Oehlmann and Pereira (1995) assessed seakeepingperformance of SWATH by calculating ship motions and selecting criteria for volun-tary and involuntary speed reduction as well as crew comfort. On this basis theyevolved operability index and seakeeping performance index. The achievable speedsat each heading (limited by seakeeping performance criteria) plotted in polar diagramgive the navigable zone for each sea state. Kuteynikov and Lipis (2000) proposeddetermining seakeeping indices considering short-term and long-term seakeepingcharacteristics. Short-term characteristics give characteristics in a given seaway whilelong-term characteristics consider probability of occurrence of the seaway over largerperiod of time. 3. Methodology for assessment of operability indexThe method is based on short-term evaluation of ship performance by obtainingvarious responses at different speeds and headings in the specified sea conditions,as defined by their directional sea spectra. The ship response spectra are thusobtained. For any specific set of performance criteria, the speeds at which the criteriawill be met can then be determined for any combination of sea-state and ship head-ing.Operability Index (OI) is defined as the ratio of navigable area limited by thechosen limits of operation pided by the total area in a polar plot. The polar plotrepresents angle of heading demarcated by radial lines and speeds represented byconcentric circles. Shaded areas indicate locations of such speed and heading combi-nations where chosen limits of operation have been exceeded. Mathematically,Operability Index is defined asOI pi× pn × pmwhere piis the local probability within each elemental area that ship’s function canbe accomplished (for any distribution of heading and speed) and pn,pm are the prob-able fractions of time that the ship will travel at each combination of speed andheading angle, respectively.4. Choice of limiting values of criteria for seakeeping performanceIn all cases criteria for seakeeping performance analysis of SWATHs are baseddirectly or indirectly on limiting values of roll, pitch, vertical acceleration, slammingand deck wetness. With regard to human habitability and comfort motion sicknessis a derived parameter.4.1. Governing criterion for roll, pitch and vertical accelerationSeasickness depends on the vertical accelerations, their frequency and the exposuretime. Universal standards of limiting values as applied to SWATH vessels are at anevolutionary stage. McCreight (1987) used a limiting value of 8° for roll and 0.4gfor vertical acceleration (all figures mentioned here are significant single amplitude—SSA) while investigating performance of SWATH ships in transit condition. Sandi-son et al. (1994) investigated the performance of T-AGOS 19 (reconnaissanceSWATH vessel) using the above criteria and in addition, a limiting horizontal accel-eration value of 0.2g. STANAG (NATO Standardization Agreement) uses 0.55g forsignificant amplitude of vertical acceleration at forward perpendicular. For heavymanual work, a limiting criterion of 0.125g is prescribed for vertical accelerationand 4° for roll.By the nature of geometry of SWATH ships, roll occurrence is small and thefrequency at which it occurs is quite low and well de-linked from the frequenciesin a natural seaway. Rolling, when present may contribute to motion sickness con- sidering the above factors. RMS roll angle amplitude is the governing criterion asso-ciated with motion sickness. However, it is the vertical acceleration component aris-ing from motions that induces motion sickness. The roll criterion has been moderatedto a value of 8° which looks more realistic in the context of low frequency rollmotion that a SWATH ship typically undergoes. A limiting value of 0.40g has beenset for vertical acceleration for the SWATH.Pitching motion is detrimental to human effectiveness since it contributes to verti-cal acceleration. Therefore it is important to set correct upper limits for pitchingmotion. A SWATH ship would be smaller in length compared to a mono-hull onthe basis of constant displacement. SWATH vessel also has characteristically lowerfrequency of pitch oscillation and hence higher limit of pitch amplitude is conceiv-able in the limiting case.Olson (1977) fixed 2.4° rms pitch as an operational limit on ship subsystems suchas replenishment-at-sea equipment, if there exists no specific consideration of humaneffectiveness. McCreight (1987) and Sandison et al. (1994) have assumed an upperlimit of 30for pitch to assess the seakeeping performance of SWATH ships. In thepresent case, transit conditions are assumed and rms pitch value is set at 3°.4.2. Governing criterion for slamming accelerationSlamming induces local acceleration and therefore the ship experiences vibratoryresponse and some times, high hull bending stresses. A SWATH vessel with roundedunderwater displacement hull is possibly subjected to lesser slam acceleration. How-ever in association with higher speed capacity of SWATH in rough weather, a valueof 0.55g is set as the operational limit.4.3.