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1 (1)where, Bi=the position vectors of polygon vertices, these are the coarse coordinateschosen on the basis of the distribution of areas of sections, along a frame; ; Ni,k=nor-malized B-spline basis functions which assume the values; Ni,k(t)=1if xi t xi+1,0otherwise; Ni,k(t) (t xi)Ni,k 1(t)xi k 1 xi (xi k 1)Ni 1,k 1(t)xi k xi 1; xi=elements of a knotvector, xi xi+1,these give flexibility to the curve by appropriate choice; t=parameter,tmin t tmaxwhere tmin corresponds to minimum value of knot vector, typically zero where Ni,k(u) and Mj,l(w) are the B-spline basis functions in the bi-parametric u andw directions, respectively. Typically for the SWATH form, u and w can be takenalong body frames and waterlines.The basis functions are given byNi,k(u) 1if xi u xi+10 otherwiseNi,k(u) (u xi)Ni,k 1(u)xi+k 1 xi (xi+k u)Ni+1,k 1(u)xi+k xi+1andMj,l(w) 1if yj w yj+10 otherwiseMj,l(w) (w yj)Mj,l 1(w)yj+l 1 yj (yj+l w)mj+1,l 1(w)yj+l yj+1where xi, yjare the elements of knot vectors; Bi,jare the vertices of a defining polygonnet enveloping the hull shape in a set of coarse coordinates as chosen already onthe basis of distribution of area; n and m are one less than the number of definingpolygon vertices in the u and w parametric directions; and k and l are the order ofthe B-spline curve in u and w directions respectively.The surface as generated above is directly interfaced with AutoCAD to get thevarious 3D views as required. Conventional grid of waterlines can be obtained bysuitable sorting of the obtained surface data. The resulting bi-quintic B-spline surfacerepresenting three different hull forms are shown in Figs. 2, 3 and 4.5.3. Evaluation of ship performanceOnly short-term evaluation has been considered in the present study and this hasbeen considered adequate for assessing the different forms in assumed sea conditions.The variants of SWATH forms are analyzed to obtain hydrodynamic loads andmotions using the package SEDOS (Soeding, 1988). Six degrees of freedom motionsand internal loads for twin hull ships are calculated on the basis of strip method.Hydrodynamic interactions between both hulls are taken into account. The methodperforms integration over ship length, excluding areas of sharp discontinuities suchas transom ends or at the ends of struts. Inputs for calculating hydrodynamic loadsand motions are given in the form of geometrical description for demi-hull, massbased properties, coordinates of points for which motions are to be obtained, shipspeed and spectrum parameters. Outputs obtained are the excitation and radiationforces, non-dimensionalized values for six degrees of freedom for regular waves,significant amplitudes in natural short crested seaways, motions of selectable fixedpoints on the ship and relative motions between ship-fixed points and water surface.Stationary condition responses as well as motions in speed conditions in regular headseas are considered in the present study. 1085 V.I. Beena, V.A. Subramanian / Ocean Engineering 30 (2003) 1077–1106Seakeeping predictions were performed for short-crested irregular seas, utilizingJONSWAP wave spectra model. Performance in sea state 4, 5 and 6 were estimatedto obtain the seaworthiness characteristics.6. Parameter based performance evaluation of loads and motion responseKeeping strut water plane area constant, 20 variants of underwater displacementhull have been systematically generated. In addition, the semi-SWATH was alsoinvestigated. The objective primarily is to predict the trend of changes due to para-meters of length, basic section shape, and taper of the hull due to modified distri-bution of cross sectional area along the length. The cases are graphically presentedin Table 2.The results were obtained for responses and dynamic effects in short crested sea-way. For this purpose the spectral parameters of the seaway have to be defined. Theinputs contain the following spectral parameters, viz. significant wave height, peakperiod and directional spreading function. The assumed data is given in Table 3.Seakeeping predictions were performed for the short crested irregular seas, definedby JONSWAP wave spectra. Table 4 shows environmental data pertaining to differ-ent sea-states.The methodology for obtaining the Seakeeping Operating Envelope (SOE) is illus-trated in the case of SWATH with length 55 m and slenderness ratio 0.083. Thewave spectrum for sea state 5 is shown in Fig. 5. The derived significant responsesare reproduced in Tables 5–10.Similarly slamming accelerations given in Table 8, show occurrence of valuesexceeding the set limit of 5.4 m/s2(0.55g). They occur in head sea conditions athigh speeds.Significant roll responses given in Table 9 indicate that they do not exceed theset upper limit value of 8° in any case. Vertical acceleration also does not exceed0.4g as given in Table 10. In no case, the condition, ((H1/3 Hkr) 0) occurs. Fig.2(d) shows the SOE obtained with these data.The transition of favourable zones of operation to unfavourable zones occurs dueto speed effect. Primarily the ship’s frequency of response may get shifted into effec-tive frequencies where the sea spectral energy occurs. Case illustration is providedin Fig. 7 The occurrence of pitch response in head sea results in predominantlyinoperable condition as seen in the polar plot. The response obtained in regular wavesis plotted after correction to a scale of encounter frequency along with plot of wavespectrum. It is obvious that in all the five cases the input sea spectrum overlapsignificantly resulting in large pitching motions. Hence predominantly shaded areasoccur in the polar plot in head sea condition.Similarly the effect in following sea condition is brought out in Fig. 8. At zerospeed the spectral overlap is maximum, hence resulting in shaded area around theinnermost circle in the polar plot. Beyond 10 knots, the spectral plots do not overlap.Hence the polar plot shows unshaded area beyond speed of 10 knots in followingsea condition. The results of the analysis are given in the form of polar plots inFig. 6–.