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Criteria prescribed for performance limitsThe analysis is performed on an assumption of transit condition associated withoceanographic research. This mission consists of general point-to-point transit to andfrom the research area. Performance evaluation is limited to sea-state 5, and equalprobability of all ship headings is assumed (Table 1).Table 1Prescribed performance limits for SWATHGoverning criteria Performance limitSignificant roll amplitude 8 degSignificant roll amplitude 3 degVertical acceleration at FP 0.40gSlamming acceleration 0.55gDeck wetness (H1/3 Hkr) m when positiveaaH1/3 is the significant wave height, and Hkr is critical wave height such as corresponding to deckheight from water surface. 5. Methodology for hull form generation and performance assessmentA computer aided numeric form of bi-quintic surface generation has beendeveloped and adopted (Subramanian and Beena, 2002). The surface is evolved onthe basis of prime owner’s requirements of size (displacement) and speed. Brieflystated, the scheme employs Chebychev polynomial and coefficients to arrive at opti-mal distribution of area of cross section of underwater displacement hull as well asdistribution of strut thickness (McCreight, 1987). In order to assess the seaworthi-ness, three hull forms conforming to same length, displacement and distribution ofstrut thickness and hull cross sectional area, but differing in basic hull shapes havebeen designed by the above scheme. The hull shapes conform to ‘circular’, ‘elliptical’and ‘golf club’ shaped sections respectively for constant values of displacement(1750 tons), ratio of volume of displacement hull and strut (0.8:0.2), spacing of hulls(15 m), length of hull (LB=80 m), length of strut (0.85×LB), a selected range ofmaximum cross sectional area of displacement hulls, constant maximum width ofstrut, and constant air gap between waterline and cross deck.For design purpose, to generate the hull form, the upper hull and strut are de-linked from the lower hull. Thus different underwater hull forms are evolved forgiven water plane area and fixed upper hull.5.1. Scheme for hull form generationBased on the minimum inputs of vessel displacement and speed, other parametersbased on geometry, are generated and employed in a convergent scheme to obtaindistribution curves for the strut thickness and displacement hull sectional area. Geo-metrical coordinates constituting the polygon net for each frame are formed usingthese distribution curves. The obtained geometrical coordinates form the controlpolygon points for the surface generation. The general B-spline equations (Rogersand Adams, 1990) are used for the surface generation to evolve a bi-quintic surface(Subramanian and Beena, 2002; Subramanian and Suchithran, 1999). The salientfeature of the method is that desired hull geometry characteristics are in-built in theform by choice of sectional areas and strut width based on the ‘optimal’ Chebychevscheme. Secondly, the points generated are tentative coarse grid points that form thepolygon net enabling ab initio design of the surface. They play the role of effectiveweighting functions, which locally influence the formation of a continuous 3D sur-face to represent the smooth hull form. By modifying the coarse grid points, differenthull forms can be rapidly evolved for evaluation. Thus for a given sectional areadistribution and strut thickness distribution of SWATH the polygon net is formedfirst, and thereafter a B-spline based surface is formed. The scheme is shown inFig. 1.5.2. B-spline based surface generationThe forms evolved are shown in Figs. 2, 3 and 4 and the mathematical techniquebacking the development is briefly described. Bi-quintic B-spline surface represen- tation requires polygon net points, which may lie in the plane of either ship stations(frames) or waterlines. They are the input data (Bi) and provide added features ofcontrollability. Multiple polygon vertices [Eq. (1)] help formation of cusps whererequired and this feature of introduction of multiplicity of points where knuckles areformed, is incorporated in the algorithm.The position vectors of a point along a frame on the ship (hence representativeof curves in a plane) are given in terms of a single parameter t, as follows:P(t) n 1i 1BiNi,k(t) tmin t tmax,2 k n