csnk, 04 Int. J. Nav. rchit. Ocean Eng. (04) 6:700~74 http://dx.doi.org/0.478/ijnoe-03-006 pissn: 09-678, eissn: 09-6790 Effects of hull form parameters on seakeeping for YTU gulet series with cruiser stern Ferdi akici and Muhsin ydin Yildiz Technical University Faculty of Naval rchitecture and Maritime, Istanbul, Turkey STRT: This study aims to identify the relations between seakeeping characteristics and hull form parameters for YTU Gulet series with cruiser stern. Seakeeping analyses are carried out by means of a computer software which is based on the strip theory and statistical short term response prediction method. Multiple regression analysis is used for numerical assessment through a computer software. RMS heave-pitch motions and absolute vertical accelerations on passenger saloon for Sea State 3 at head waves are investigated for this purpose. It is well known that while ship weight and the ratios of main dimensions are the primary factors on ship motions, other hull form parameters ( P, WP, VP, etc.) are the secondary factors. In this study, to have an idea of geometric properties on ship motions of gulets three different regression models are developed. The obtained outcomes provide practical predictions of seakeeping behavior of gulets with a high level of accuracy that would be useful during the concept design stage. KEY WORDS: Ship motions; Gulets; Hull form parameters; Multiple regression method. NOMENLTURE O P VP WP D Fn H /3 k yy Overall breadth Waterline breadth lock coefficient Prismatic coefficient Vertical prismatic coefficient Waterline area coefficient Depth Froude number haracteristic wave height Gyration radius for pitch motion L Longitudinal position of center of buoyancy L F Longitudinal position of center of floatation L O Overall length L P Length between perpendiculars L Waterline length T Draught T m Modal wave period Displacement volume Displacement force µ ngle of encounter REVITION LIST ITT International towing tank conference SS Sea state RO Response amplitude operator STNG Standardization agreement RMS Root mean square YTU Yildiz technical university orresponding author: Ferdi akici, e-mail: fcakici@yildiz.edu.tr This is an Open-ccess article distributed under the terms of the reative ommons ttribution Non-ommercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Int. J. Nav. rchit. Ocean Eng. (04) 6:700~74 70 INTRODUTION Existing gulets are used for pleasure trips today. Therefore it became significant to conduct a study in order to discover their hydrodynamic characteristics. systematic series of gulet hull forms with cruiser stern is developed in order to investigate their performance (ydın, 03). ertain processes could be made to understand seakeeping characteristics of the gulets by making use of several methods. lthough the strip theory is the quickest and relatively most accurate one it has restrictions because of its theoretical assumptions. It has been most preferred tool during conceptual design stage. Due to its theory is linear; solutions are more realistic for slender hulls and low Froude numbers. However, strip theory has been widely accepted and a large number of computer codes are developed. While resistance and power outputs are sensitive to local changes of hull form, seakeeping matrix is less sensitive local changes of hull form. Seakeeping performance usually depends on main dimensions and their proportions, hydrostatic values and weight distribution. For this reason, seakeeping phenomenon must be evaluated in conceptual design stage (Şaylı et al., 007). Several studies can be found in technical literature about effects of ship geometry on seakeeping characteristics. ales performed a criteria free rank study for 0 displacement- normalized destroyers by using six form parameters. ased on the general definition of seakeeping rank, eight seakeeping responses were computed for each hull form. The responses were pitch, heave, ship to wave relative motion at Station 0 and 0, bottom slamming at Station 3, absolute vertical acceleration at Station 0, heave acceleration and absolute vertical motion at Station 0. nalyses were performed in long crested head seas for five speeds each for five modal periods (ales, 980). Kükner and Sarıöz made calculations for high speed vessels in their study. They investigated main dimensions and seconder hull form parameters effect on vertical motions (Kükner and Sarıöz, 995). rown conducted a study for gulet type boats in terms of resistance and seakeeping. Then he tried to present optimum hull parameters for gulets (rown, 005). Şaylı and others showed the effects of hull form parameters on vertical motions for fishing vessels by using multiple regression techniques (Şaylı et al., 007). Şaylı and others, in their next study, performed the same configuration by using non-linear regression techniques (Şaylı et al., 009). Results were very adoptable with each other. Özüm and others observed the effect of hull parameters for high speed hull forms during conceptual design stage. They explored main dimensions and secondary form parameters make the main contribution to ship motions (Özüm et al., 0). Fig. ody Stations, profile and waterlines of a gulet in the series.
70 Int. J. Nav. rchit. Ocean Eng. (04) 6:700~74 In this study, gulet type pleasure boats were examined in terms of seakeeping properties. lthough gulets were built in traditional ways previously, these crafts are built with modern technics in recent years. study was conducted with the purpose of developing an original gulet series with cruiser stern without destroying its character. First, cruiser stern gulet hull forms with different geometric design block coefficients ( ) were designed by the author with the information gained during the technical visits. These hull forms were produced by preserving conventionalism. Detailed information can be found in related paper. (ydın, 03) ody Stations, profile and waterlines of a gulet in the series are shown in Fig.. The hull form parameters of YTU Gulets are tabulated in Table. For comparison purposes Table is constructed to show the dimension and displacement ranges of existing gulets in Turkey and YTU Gulets. Table Main dimensions and some geometric properties of YTU gulets with cruiser stern. Gulets L O (m) L WZ (m) O (m) (m) T(m) D(m) M (W)(ton) G 5.976 4.839 4.389.558.634 0.56 0.39.495 G 6.774 5.036 4.57.6.74 0.6 0.403 5.78 G3 7 3.573 5.4 4.746.665.845 0.68 0.44 9.434 G4 8 4.37 5.404 4.95.76.99 0.69 0.46 34.8 G5 9 5.70 5.575 5.078.8 3.090 0.74 0.46 39.37 G6 0 5.968 5.739 5.37.859 3.85 0.80 0.435 44.60 G7 6.766 5.896 5.39.95 3.33 0.8 0.436 50.776 G8 7.565 6.046 5.54.996 3.4 0.86 0.444 57.00 G9 3 8.363 6.89 5.688.040 3.499 0.9 0.45 63.687 G0 4 9.6 6.37 5.83.9 3.69 0.9 0.45 7.307 G 5 9.960 6.460 5.973.70 3.7 0.98 0.459 78.97 G 6 0.758 6.587 6..0 3.790 0.303 0.466 87.07 G3 7.557 6.70 6.49.95 3.93 0.304 0.464 96. G4 8.355 6.88 6.385.333 3.989 0.309 0.470 05.330 G5 9 3.54 6.94 6.59.370 4.06 0.34 0.475 4.966 G6 30 3.95 7.05 6.65.45 4.79 0.34 0.473 5.839 G7 3 4.750 7.56 6.784.487 4.49 0.39 0.477 36.574 G8 3 5.549 7.58 6.96.5 4.37 0.34 0.48 47.866 G9 33 6.347 7.356 7.047.60 4.49 0.34 0.478 60.559 G0 34 7.46 7.45 7.78.633 4.493 0.39 0.48 73.03 G 35 7.944 7.543 7.30.665 4.556 0.334 0.484 86.03 Table comparison between existing gulets and YTU gulets with cruiser stern. Existing gulets with cruiser stern YTU gulets with cruiser stern L O (m) 8-33 5-35 O (m) 5.400-7.800 4.839-7.543 D(m).350-4.0.634-4.556 T(m).650 -.760.558 -.665 0.30-0.35 0.56-0.334 WP 0.705-0.80 0.738-0.83 p 0.646-0.730 0.654-0.689 (kn) 343.35-50.55 0.86-85.67
Int. J. Nav. rchit. Ocean Eng. (04) 6:700~74 703 Effects of geometrical features of different YTU Gulets on their seakeeping characteristics in terms of the following three responses are investigated: Heave motion Pitch motion bsolute vertical acceleration at the passenger saloon Location of the passenger saloon is shown in the Table 3: Table 3 Location of the passenger saloon. Longitudinal distance from after end point (m) L O 0.4 Transverse distance from centerline (m) 0 Height from the keel (m) D.0 Design database Displacement forces of the gulets should be brought to equal level for fair comparison of effects of geometric characteristics on specified ship motions. This value is 774.7 kn. Thus the design database is built with the hull forms of displacement normalized YTU Gulets those are given in Table 4: Table 4 Hull form parameters for analyses. Gulets L / /T L / /3 WP P VP L F /L O L /L O G.79.87 4.343 0.738 0.654 0.347 0.49 0.509 G.795.836 4.389 0.73 0.650 0.358 0.49 0.505 G3.860.850 4.43 0.75 0.647 0.369 0.484 0.497 G4.94.789 4.460 0.70 0.646 0.373 0.48 0.49 G5.987.804 4.50 0.77 0.644 0.383 0.478 0.487 G6 3.049.87 4.540 0.75 0.643 0.39 0.476 0.484 G7 3.0.763 4.565 0.74 0.644 0.393 0.473 0.480 G8 3.70.776 4.60 0.74 0.644 0.40 0.47 0.479 G9 3.8.788 4.636 0.76 0.645 0.407 0.470 0.476 G0 3.86.739 4.659 0.78 0.647 0.407 0.469 0.475 G 3.34.753 4.69 0.7 0.648 0.4 0.468 0.475 G 3.396.766 4.73 0.77 0.650 0.46 0.467 0.476 G3 3.450.73 4.743 0.734 0.654 0.44 0.464 0.476 G4 3.50.737 4.773 0.74 0.657 0.46 0.464 0.477 G5 3.55.75 4.80 0.750 0.660 0.48 0.468 0.479 G6 3.60.73 4.89 0.759 0.665 0.44 0.465 0.48 G7 3.648.78 4.846 0.770 0.668 0.44 0.470 0.484 G8 3.694.74 4.87 0.78 0.673 0.44 0.47 0.487 G9 3.739.709 4.888 0.794 0.679 0.408 0.473 0.490 G0 3.78.76 4.9 0.808 0.684 0.407 0.475 0.494 G 3.83.743 4.935 0.83 0.689 0.405 0.477 0.498
704 Int. J. Nav. rchit. Ocean Eng. (04) 6:700~74 SEKEEPING LULTIONS Seakeeping performance is evaluated for head waves ( µ =80 ) and for Fn =0:0.5:0.3 in this paper. Hydrodynamic coefficients are calculated by using Frank lose Fit Method for each gulet section. This solution is valid for arbitrary cross sections and the velocity potential is represented by a distribution of sources on the mean submerged cross section. In this method; green function satisfying the linear free surface boundary condition is used to represent the velocity potential. The density of the sources is an unknown function to be determined from integral equations obtained by applying the body boundary condition (Frank, 967). ross sections of the gulet (G) are shown in Fig.. Fig. Sections of the G and close fit points. The assessment of seakeeping performance of a pleasure craft in a specified sea state is related to four elements: Ship geometry Weight distribution on ship Transfer functions (RO) in regular waves Wave spectrum s a result of these interactions, determination of ship responses can be obtained. Gulet response characteristics The first step for determination of the seakeeping performance is to detect the motion response amplitudes and phase lags in the frequency domain for all six degrees of freedom. Then ROs can be executed for each specified response such as heave motion, velocity and acceleration. RO graph of G is shown in Fig. 3 in case of zero speed and head waves. It should be pointed out that there is a strong resonance danger in existence of restoring effect such as heave and pitch motion. Definition of seaway Ship motions in irregular waves should be investigated due to absence of regular waves in nature. It is important to get ship motions in random waves because of the complexity of sea surface. Modeling sea is possible by using some statistical methods. Irregular sea can be expressed by using wave spectra that is composed as regards to normal distribution. Spectral density function must be known to enter short term statistical parameters. This recommended function must fit characteristic of the sea environment where gulets will sail. It is used parameter ITT (retschnider) wave spectrum in analyses which is proposed in STNG 494 documents by reason of gulet type boats mostly operate in East Mediterranean Sea. nalyses are performed at sea state 3. haracteristic wave height and modal period of sea state 3 are shown in Table 5:
Int. J. Nav. rchit. Ocean Eng. (04) 6:700~74 705 Fig. 3 Heave transfer function for Fn =0, for G. Table 5 haracteristics of east mediterranean sea at SS 3. SS H /3 (m) T m (s) 3 0.88 6.5 Prediction of motions It is very common to use D and 3D analytical methods on prediction of ship responses in operational sea environment. t the short-term analyses, average, observed and most frequent motion amplitudes are obtained by the help of response function curve which is plotted with superposition RO and wave spectrum curve (Figs. 4-6). This procedure is applied with Eq. (). Response function curve must be plotted in the case of head waves and vertical responses. Maximum Fn is taken as 0.3 because the gulets are displacement type boats and Fn is a limiting factor for the strip theory. ( ω ) ( ω ) S = S RO z e z e Z () Fig. 4 Typical RO curve.
706 Int. J. Nav. rchit. Ocean Eng. (04) 6:700~74 Fig. 5 Typical wave spectrum curve. Fig. 6 Typical response curve. MULTIPLE REGRESSION NLYSES The multiple regression equation is derived from the Least Squared Method and it is alike two variable regression analyses. Instead of a single independent variable, two or more independent variables are used to find a dependent variable values. The multiple regression equation is given Eq. (): P= + X + X + + X () 0 n n where P is and estimated dependent variable which represents RMS values of specified responses in case of head waves. Independent variables must represent dependent variables very well. Otherwise obtained results might be not adoptable. Used regression models are based on main dimensions and hydrostatic values since ship motions are generally are function of them. Therefore X, X, X n independent variables represent main dimensions and their proportions, form coefficients etc. On
Int. J. Nav. rchit. Ocean Eng. (04) 6:700~74 707 the other hand,, n coefficients are regression coefficients which shows how independent variables affects dependent variables. These all variables should be written in matrix format in Eq. (3) to calculate regression coefficients. X x x m x x xn xnm m = P p p pn = 0 m = (3) Eq. (4) must be solved to find matrix of the regression coefficients. T T ( ) ( ) = X X X P (4) T while m shows number of independent variables n shows number of equation. X represents transpose of X matrix. Number of independent variables, m, is determined from selected regression model. In this respect, multiple regression coefficients are computed by using regression solver software with a very high R. equations are solved for each response and regression model. Recommended regression models are given next chapter. Recommended regression models Three different regression models are presented for the purpose of determining effects of independent variables on dependent variables. These regression models are given in Table 6. Dependent variables which are used in regression analyses are RMS responses of specified ship motions at SS3 for displacement normalized gulets. omputed RMS values represent most frequent motion amplitudes at SS3. esides, computations are repeated for each model for seven different Froude number ( Fn =0:0.05:0.3). Table 6 Used models for regression analyses. Model number Used parameters L /, / L /, / 3 L /, / /3 T, L / ( ) T, / ( /3 ) T, / ( /3 ) L, WP, VP, P L, WP, VP, P, L / L O, LF / L O while Model consists of only main dimension proportions, Model additively consist of WP, VP and P hydrostatic form coefficients. Model 3 contains main dimension proportions, hydrostatic form coefficients and L - L F locations as addition. dequate consideration of models is extremely important to evaluate multiple form parameters at this kind of analyses. Therefore number of models is selected as three. Multiple regression equations for Model ; L L RMS Heave = + 0 /3 3 + (5)
708 Int. J. Nav. rchit. Ocean Eng. (04) 6:700~74 L L RMS Pitch = + 0 /3 3 + (6) L L RMS Vertical cce. t the Saloon = + 0 /3 3 + (7) Multiple regression equations for Model ; L L RMS Heave = 0 + + + /3 3 + WP 4 + VP 5 + P 6 T (8) L L RMS Pitch = 0 + + + /3 3 + WP4 + VP5 + T (9) L L RMS Vertical cce. t the Saloon = 0 + + + /3 3 + WP4 + VP5 + T (0) Multiple regression equations for Model 3; L L RMS Heave = 0 + + + /3 3 + WP 4 + VP 5 + + L 7 + LF 8 T () L L RMS Pitch = 0 + + + /3 3 + WP 4 + VP 5 + + L7 + LF 8 T () L L RMS Vertical cce. t the Saloon = 0 + + + /3 3 + WP4 + VP5 + + L7 + LF8 T (3) omputed regression coefficients can be found Tables 7-5. While Tables 7-9 show regression coefficients for Model, Tables 0- show regression coefficients for Model. Finally Tables 3-5 present regression coefficients for Model 3. Table 7 Regression coefficients for heave motion for Model. L L RMS Heave = + 0 /3 3 + Fn 0 3 R 0 0.0545-0.057-0.086 0.0736 0.997 0.05 0.0856-0.047-0.000 0.0648 0.9906 0. 0.0575-0.057-0.086 0.0736 0.997 0.5-0.0330-0.076-0.055 0.0 0.998 0.0-0.0893-0.0858-0.0334 0.396 0.970 0.5-0.304-0.38-0.0497 0.93 0.9668 0.30-0.4800-0.709-0.0638 0.309 0.9504
Int. J. Nav. rchit. Ocean Eng. (04) 6:700~74 709 Table 8 Regression coefficients for pitch motion for Model. L L RMS Pitch = + 0 /3 3 + Fn 0 3 0-7.3040 -.3830-0.8588 4.0664 0.9839 0.05-9.7393 -.976 -.68 5.677 0.9748 0. -.9409-3.4966 -.363 6.437 0.9654 0.5-6.7037-6.0890 -.495.7 0.8807 0.0-4.376-4.0955 -.6998 7.66 0.9578 0.5-4.7846-4.065 -.7856 7.4688 0.9574 0.30-3.3589-3.8644 -.6367 6.877 0.968 R Table 9 Regression coefficients for vertical acceleration at saloon for Model. L L RMS Vertical cce. t the Saloon = + 0 /3 3 + Fn 0 3 0-0.057-0.355-0.0367 0.950 0.9950 0.05-0.0-0.994-0.0779 0.303 0.995 0. -0.4558-0.758-0.069 0.4356 0.9939 0.5-0.6609-0.3546-0.57 0.576 0.9884 0.0 -.044-0.4574-0.004 0.765 0.9830 0.5 -.4407-0.5643-0.498 0.963 0.9709 0.30 -.844-0.6769-0.3054.698 0.955 R Table 0 Regression coefficients for heave motion for Model. L L RMS Heave = 0 + + + /3 3 + WP 4 + VP 5 + P 6 T Fn 0 3 4 5 6 0 0.89-0.0040 0.0039-0.0088-0.088 0.0036 0.437 0.9950 0.05 0.0664-0.03-0.04 0.005-0.0536 0.073 0.30 0.999 0. 0.9-0.0040 0.0039-0.0088-0.088 0.0036 0.437 0.9950 0.5 0.3340 0.003-0.000-0.0094-0.004-0.0453-0.44 0.9933 0.0 0.877 0.000-0.0-0.053 0.03 0.468 0.083 0.986 0.5-0.677-0.0806-0.035 0.089-0.054 0.87 0.387 0.9853 0.30-0.359-0.05-0.036 0.399-0.88 0.67 0.4888 0.983 R
70 Int. J. Nav. rchit. Ocean Eng. (04) 6:700~74 Table Regression coefficients for pitch motion for Model. L L RMS Pitch = + 0 /3 3 WP 4 VP 5 + + + + Fn 0 3 4 5 6 0-8.688 -.49 -.0390.9659 0.8044 0.8044 5.903 0.999 0.05-0.074 -.804 -.3376 3.939.5473 9.0038 6.5744 0.9904 0.0-9.909 -.885 -.504 3.330.334 0.5508 6.309 0.9877 0.5-6.4370 -.9344.399.873 -.850-44.4930-5.9979 0.9389 0.0-9.5078 -.8879 -.6999 3.09.480.9083 6.655 0.987 0.5-7.874 -.5469 -.6897.4699 3.0336.330 4.46 0.988 0.30.6896-0.0944-0.309-0.735 -.0444-0.735 3.700 0.9533 R Table Regression coefficients for vertical acceleration at saloon for Model. L L RMS Vertical cce. t the Saloon = + 0 /3 3 WP 4 VP 5 + + + + Fn 0 3 4 5 6 0-0.8767-0.79-0.0393 0.350-0.3338 0.0333 0.98 0.9960 0.05 -.753-0.340-0. 0.4669-0.89 0.4796.064 0.9966 0.0-0.859-0.370-0.45 0.3768 0.060 0.8430 0.808 0.9965 0.5-0.670-0.458-0.56 0.89 0.373 0.9433 0.3705 0.996 0.0-0.075-0.496-0.839 0.506 0.34.4354 0.5476 0.9940 0.5 0.88-0.9-0.04 0.034 0.4746.80 0.4603 0.997 0.30 0.8309-0.650-0.583-0.80 0.97.65 0.039 0.9877 R Table 3 Regression coefficients for heave motion for Model 3. L L RMS Heave = 0 + + + /3 3 + WP 4 + VP 5 + + L 7 + LF 8 T Fn 0 3 4 5 6 7 8 R 0-0.56-0.0543-0.005 0.0753-0.34 0.03 0.63 0.370 0.079 0.996 0.05-0.396-0.03-0.055 0.697-0.045 0.393 0.5 0.3003-0.0360 0.9950 0.0-0.53-0.0543-0.003 0.0756-0.34 0.036 0.63 0.370 0.0790 0.996 0.5 0.470 0.0064 0.006-0.030 0.0640-0.0855-0.333 0.0400-0.46 0.995 0.0 0.350-0.0-0.00-0.03 0.430 0.8-0.00 0.473-0.40 0.9890 0.5 0.046-0.066-0.074 0.0660 0.0590 0.5 0.05 0.009-0.640 0.9908 0.30 0.936-0.095 0.004 0.0006-0.050 0.0 0.306-0.337-0.088 0.9876
Int. J. Nav. rchit. Ocean Eng. (04) 6:700~74 7 Table 4 Regression coefficients for pitch motion for Model 3. L L RMS Pitch = + 0 /3 3 WP 4 VP 5 L7 LF 8 + + + + + + Fn 0 3 4 5 6 7 8 0 -.00 -.495-0.580.40.800 4.7609 3.366 -.489 -.7430 0.9954 0.05 -.49 -.750-0.850.5330.74 6.876 3.505 -.778 -.05 0.9938 0.0-0.890 -.69-0.88.39 3.555 7.955.6737-3.34 -.4976 0.99 0.5-45.733-8.38-0.6640.590-8.845-36.00-3.8 3.04-7.955 0.9660 0.0-0.30 -.5673 -.045 0.88 3.898 9.055.599-3.463 -.4797 0.994 0.5.060 -.454 -.30 0.5960 4.4055 9.7587 0.906 -.87 -.4375 0.997 0.30-3.890-4.775 -.594 7.6390 -.6 0.75 3.89 5.56-0.68 0.9873 R Table 5 Regression coefficients for vertical acceleration at saloon for Model 3. L L RMS Vertical cce. t the Saloon = 0 + + + /3 3 + WP4 + VP5 + + L7 + LF8 T Fn 0 3 4 5 6 7 8 R 0-0.7530-0.06-0.090 0.35-0.37-0.00 0.964-0.0659-0.0077 0.9960 0.05 -.5-0.3500-0.5 0.48-0.38 0.50.3 0.054 0.0364 0.9966 0.0 -.578-0.467-0.34 0.64 0.4.050 0.768 0.483-0.0698 0.9970 0.5-0.8-0.630-0.645 0.496 0.87 0.947 0.43 0.0934-0.036 0.997 0.0-0.675-0.3907-0.5 0.3907 0.459.597 0.535 0.5504-0.660 0.9949 0.5 0.093-0.99-0.459 0.839 0.6470.8736 0.068 0.4057-0.3603 0.998 0.30 0.7680-0.490-0.97-0.0354.700.6677-0.507 0.4464-0.500 0.9896 DISUSSION fter researching recommended regression models it is now possible to evaluate the effects of hull geometry on seakeeping characteristics. R-squared values which specify goodness of fit are around 0.95. It is a very good prediction on determining dependent variables. It means that independent variables represent dependent variables very well. However, when Table 8 is examined; one can see a slight decreasing R -squared value. It is determined around 0.88 and corresponds to Fn =0.5 case. This situation leads to a slight difference between strip theory and recommended models that can be seen in Figs. 6(b) and Fig. 8(b). There is no specific reason for this state due to calculation of motions is dependent of so many parameters. Hull form requirements for good seakeeping for the gulets are given in Table 6: When regression coefficients of Model are investigated the effects of main dimension proportions on ship motions are /3 seen clearly. Increasing of L / and / T values, decreasing of L / values became useful to reduce heavepitch motions and absolute vertical acceleration at saloon. In particular, being positive or negative value of regression coefficient is a solid symptom that shows how it affects. The role of the parameters given with question marks is not clear. When Model is examined it is understood that higher WP lower VP and P values are better for heave motion. It is also seen from tables that lower VP and P values are better for pitch motion and vertical acceleration. Model 3 has to be checked to obtain the influence of L and L F. These points are should be closer to bow for pitch motion. In other respects, while L should be closer stern L F should be closer bow for the sake of heave motion and vertical acceleration. If the regression coefficient tables are observed in detail the rate of influence of parameters also could be understood. omparing rate of
7 Int. J. Nav. rchit. Ocean Eng. (04) 6:700~74 influence is simply possible when each parameter is grouped each other such as separation of comparing form coefficients and L and L F. Figs. 7-9 shows the comparison between strip theory and multiple regression calculation for gulet. While Fig. 7 shows respectively heave- pitch motions and vertical acceleration for Model, Fig. 8 shows respectively heave-pitch motions and vertical acceleration for Model, Fig. 9 shows respectively heave-pitch motions and vertical acceleration for Model 3. It could be easily seen from Figs. 7-9 that RMS strip theory values for heave-pitch motions and vertical acceleration are predicted very close to multiple regression computations. Table 6 Requirement for good seakeeping. Parameters Heave Pitch Vert. cce. t Saloon L / High High High / T High High High /3 L / Low Low Low WP High?? VP Low Low Low P Low Low Low L ft from mid-ship Forward from mid-ship ft from mid-ship LF Forward from mid-ship Forward from mid-ship Forward from mid-ship Fig. 7 (a) Model - heave comparison between strip theory and regression. (b) Model - pitch comparison between strip theory and regression. (c) Model - vert. acce. comparison between strip theory and regression.
Int. J. Nav. rchit. Ocean Eng. (04) 6:700~74 73 Fig. 8 (a) Model - heave comparison between strip theory and regression. (b) Model - pitch comparison between strip theory and regression. (c) Model - vert. acce. comparison between strip theory and regression. Fig. 9 (a) Model 3- heave comparison between strip theory and regression. (b) Model 3- pitch comparison between strip theory and regression. (c) Model 3- vert. acce. comparison between strip theory and regression.
74 Int. J. Nav. rchit. Ocean Eng. (04) 6:700~74 ONLUSION The development of the effect of hull form parameters of YTU Gulets on ship motions is presented in this paper with several processes. The process started with prediction of transfer functions for different gulet forms for different Froude numbers. Then these transfer functions are combined with specified spectral curve. Finally, the effects of hull form parameters are determined by the help of multiple regression method. t the end of the study, hull form requirements for good seakeeping for the gulets are determined. The comparison between strip theory and multiple regression calculations for gulet is shown in figures. The obtained results ensure practical predictions of form parameter contribution to motions with a high level of accuracy that would be useful during the concept design stage. s a future work, the habitability indices of gulet type pleasure hulls will be investigated in terms of comfort on board. REFERENES ydın, M., 03. Development of a systematic series of gulet hull forms with cruiser stern. Ocean Engineering, 58, pp. 80-90. ales, N.K., 980. Optimizing the seakeeping performance of destroyer-type hulls. Proceedings of the 3th Symposium on Naval Hydrodynamics, Tokyo, Japan, October 980, pp.479-50. rown, D., 005. forward analysis of a gulet type hull form, Mar 398 Project and Report. Newcastle: University of Newcastle. Frank, 967. Oscillation of cylinders in or below the free surface of deep fluids, Technical Report 375. Washington D..: Naval Ship Research and Development entre. Kükner,. and Sarıöz, K., 995. High speed hull form optimization for seakeeping. dvances in Engineering Software,, pp.79-89. Özüm, S., Şener,. and Yılmaz, H., 0. parametric study on seakeeping assessment of fast ships in conceptual design stage. Ocean Engineering, 38, pp.439-447. Şaylı,., lkan,.d., Nabergoj, R. and Uysal,.O., 007. Seakeeping assessment of fishing vessels in conceptual design stage. Ocean Engineering, 34, pp.74-738. Şaylı,., lkan.d., and Ganiler, O., 009. Nonlinear meta- models for conceptual seakeeping design of fishing vessels. Ocean Engineering, 37, pp.730-74.