Maneuverability of a avepiercing igh-peed Catamaran at Low peed in trong ind akuya Oura and oshiho Ikeda Osaka Prefecture University, Japan UMMA A high-speed catamaran car ferry has sometimes serious problems on maneuvering for low speed sailing in strong wind in harbor because of large wind forces acting on its large structure above the water line. In order to clarify the maneuvering performance of such a ferry in strong wind, wind force measurements and drift speed measurements are carried out using a scale model of a wavepiercing catamaran in a towing tank with a wind generator, and performances for steady sailing in a straight direction and station keeping at zero speed in wind are calculated using the experimental data.. IODUCIO ince a high-speed catamaran car ferry has a relatively shallow draft and a large structure above the water line, a very large wind force and small hydrodynamic resistance forces from water act on the structures in air and water when the high-speed catamaran runs at low speed in strong wind. his may cause some difficulties for maneuvering in harbor. asumi et al (999) experimentally investigated maneuvering performance for a simple catamaran. In the present study, using a scale-model of a wavepiercing high-speed catamaran, the coefficients of wind forces are measured in the towing tank with a wind generator in Osaka Prefecture University. he drift resistance coefficient is also obtained by measuring the drifting speed of the model in wind in the towing tank. Using the measured wind force coefficients and drift resistance coefficient, a criterion of wind speed for the wavepiercing high-speed catamaran sailing at constant speed in a straight direction is obtained. he results are compared with those for other kinds of ships, a PCC and a tanker. he station-keeping performances of it in wind are also obtained using these experimental data. ig. /8-scale model of Incat m PC.. MEAUEME O ID OCE. EPEIMEAL OVEVIE he model used in the experiments is a /8-scale model of Incat m wavepiercing catamaran (hereafter Incat m PC) which will be introduced in a Japanese domestic route in the summer of 7. he model is shown in ig. and ig.. he principal particulars of the ship are shown in able. he schematic view of the experiment is shown in ig.3. In the experiment, wind velocity is changed as 3.8m/s, 5.7m/s, and 7.6m/s, and attack angles of the wind are changed by every 5 from to 8. Longitudinal and transverse forces and yaw moment about its mid-ship position acting on the model is measured by a three-component load cell. ig. ide and front profiles of Incat m PC. able Principal particulars. Gross onnage 8, ton L OA.6 m Length of demi-hull 5.6 m idth of demi-hull 5.8 m Breadth 3.5 m Draft 3.7 m Maximum speed 4 knot Main engine 9. k /,rpm ( 4) aterjet thrust ( 4) 33 k ( 4) ession A 83
inddirection8 indforce. DEIIIO O COEICIE he measured longitudinal and transverse forces and a yaw moment are non-dimensionalized as follows,.5 C C C (exp.) C (clal.-f) C C =, C ρ a U M Z = ρ a L LU = ρ a L U where,, and M Z denote longitudinal and transverse components of wind force, and yaw moment respectively, ρ a density of air, and L front and lateral projected areas, L length overall of the ship, U wind velocity in m/s, respectively. 3 6 9 5 8 -.5 - -.5 ind direction θ (deg.).8.6 C C C (exp.) C (cal.-f) ind generator 風洞装置ID U (m/s) θ.4. 3 6 9 5 8 ind direction θ (deg.).5 ig.3 chematic view of wind force measurement in towing tank (bird s eye view)...5 C C C (exp.) C (cal.-f).3 EUL AD DICUIO he obtained longitudinal and transverse wind force coefficients C, and C and the yaw moment coefficient C are shown in ig.4. In the figure the wind force coefficients estimated by ujiwara s method (6) are also shown. he method is an empirical one for mono-hulls. he result of the longitudinal force coefficient (C ) is asymmetrical, and smaller in head wind than in following wind. he predicted result by ujiwara s method can estimate it in fairly good accuracy in head to beam wind, but underestimates it in quarter and following wind. his difference may be caused by the catamaran shape with a tunnel. he transverse wind force coefficient C is shown in the middle figure in ig.4. he result is also asymmetrical, and has a peak near at 4 degrees of wind direction. his peak may be caused by the lift forces acting on two demi-hulls. he predicted results by ujiwara s method overestimates the measured one by ~3% in wide range of beam wind. As shown in the bottom figure in ig. 4, the measured yaw moment due to wind shows an almost symmetrical shape. he predicted result underestimates the measured one in wide range of head wind. In ig.5, wind forces and its directions acting on Incat m PC in m/s wind are shown. he wind force direction is different from the wind direction. hese are caused by the lift force components of wind forces acting on the hulls as well known. 3 6 9 5 8 -.5 -. -.5 -. ind direction θ (deg.) ig.4 Measured wind force coefficients of Incat m PC for various wind direction with predicted result by ujiwara s method. 9 6 5 3 (ton) 5 8 5 ig.5 Measured wind force vectors acting on Incat m PC in m/s wind. 3 ind velocity m/s 6 9 ession A 84
.4 MEAUEME O DI PEED I ID he model floating in calm water in the towing tank is experienced by steady wind generated by a wind generator as shown in ig.6. he model is free only in the direction of wind. he wind speeds are changed as 3.8m/s, 5.7m/s and 7.6m/s, and the wind direction are changed from to 8. ig.6 chematic view of drift speed measurement in wind(side view) In ig.7, the measured drift speeds, Us, are shown. In the figure, βshows the direction of drift motion. he βis defined to be zero when ship drifts in straight forward direction of the ship (bow direction). ince the wind force should be balanced with the drift force, the following equilibrium equation can be obtained. By solving the equation, the drift resistance coefficient, C D, can be obtained. ind 風洞装置ind generator ind force = ρ U C where denotes lateral projected area of a submerged demi-hull, U drift velocity, ρ w density of water, respectively. Drift speed (m/s).5.4 ID D 検力計 Us ind force Drift resistance eynolds number and roude number, the constant value can not be used there. herefore, in the following calculations, the C D values at drift angle above 3 are used as a function of only drift angleβ..5.5.5 CD 3 6 9 5 8 Direction of drift β (deg.) ig. 8 Obtained drift resistance coefficient C D of ICA m PC for various drift direction (β= when the ship drift in forward (bow) direction). 3.AEME O MAUEVEABILI O ICA m PC I OG ID 3. CIEIA O AIG AILIG I ID he operable criteria of wind speed for Incat m PC sailing in straight direction at constant speed when the vessel is encountered by steady wind of speed of U w (m/s) is calculated. he ship is assumed to sail at a constant speed of Us (m/s), in constant drift angle β, by a thrust force of and helm angle of δ of the steering nozzles of the waterjet propulsions as shown in ig. 9. U β u θ 風速 U.3. v G r. ind speed 7.6m/s ind speed 5.7m/s ind speed 3.6m/s 3 6 9 5 8 Direction of drift β (deg.) ig. 7 Measured drift speed in wind for various drift angle (β=8 -θ). In ig. 8, the obtained drift resistance coefficients are shown. he maximum value of the coefficients appears at aroundβ=9- and reaches about.3. his is because that the two demi-hulls create large eddy making resistances. ince C D at β= must depend on ig.9 Coordinate ystem he equilibrium of all forces acting on the ship in the directions of x, y and yaw gives the following equations. ( β ) + ( θ ) + ( δ ) = ( β ) + ( θ ) + ( δ ) = ( β ) + ( θ ) + ( δ ) = δ () ession A 85
where, and denote hydrodynamic force acting on submerged hulls, wind force and thrust force in x direction., and denote those in y direction and, and in yaw direction, respectively. hese forces and moment can be calculated as follows, respectively. 3 = ρ ( U cos β ) = ρalu C = cosδ = ρ LU = ρalu C = sinδ ' {( β ) + C sin β} β C D 4 K (=Uw/Us) 3 K(=Uw/Us) 7 6 5 δ=-3(deg.) δ=-(deg.) δ=-(deg.) 3 6 9 5 8 ( 向い風 ) 風向角 θ(deg.) (ead wind) ind direction θ(deg.) (ollowing ( 追い風 wind) ) ig. atio of wind speed to ship speed, K, when Incat m PC sails in straight direction in constant speed in various wind directions at helm angles of -3, - and - degree. = ρ LLLU = ρalllu = ( L ) ' β C sin β β (deg.) 5 5 δ=-3 where denotes displacement volume, L, and L denote lateral projected area of the submerged demi-hull, front projected area above the waterline, and lateral projected area above the waterline respectively, L and L L denote the distance from the mid-ship and length of waterline, respectively. In the calculations, Inoue s formula (97) is used for. and the experimental results of the resistance test of a demi-hull by Okada (998) is used for C. By numerically solving the equilibrium equations, K value (=U /U ) which is the ratio of wind speed to ship speed, can be obtained for various helm angle of the waterjets (anaka et al (98) and ezaki (98). In igs. -, the calculated results for sailing straightly in wind are shown. he K values shown in ig. are the results for helm angle of the waterjet of, and 3 degrees. he results demonstrate that K value becomes the minimum at wind direction of 4-5 degrees. he K value at the maximum helm angle of the waterjet, -3 degrees, shows a critical boundary line for sailing straightly at a constant speed. he minimum K value of critical boundary is about three. his means that the ship can sail in a straight direction at a constant speed of about /3 of wind speed. e can find the minimum sailing speed if wind speed and direction are given using the critical boundary line. As an example, the lee-angle, or drift angle of the ship running at m/s or two knots, at helm angle of the waterjet of -3 degrees is shown in ig.. It should be noted that the wind speed changes with each wind direction which corresponds to the K value for δ=-3 in ig... 5 3 6 9 5 8 ind direction θ(deg.) ig. esult of drift angle β when Incat m PC sails at m/s in a straight direction in wind with maximum helm angle,δ=-3 of waterjet. (kgf.) 4 8 6 4 δ=-3 3 6 9 5 8 ind ind direction direction θ(deg.) ig. esult of thrust when Incat m PC sails at m/s in a straight direction in wind with maximum helm angle,δ=-3 of waterjet ession A 86
K(=Uw/Us) K (=Uw/Us) Incat m PC anker (full load) PCC (ballast) 33 ead wind (deg.) 9 (m/s) 3 Incat m PC hrust % hrust 8% hrust 5% 8 6 6 3 3 6 4 7 9 3 6 9 5 8 風向角 (deg.) ind direction θ(deg.) 4 ig.3 Comparison of critical value of K of Incat m PC with other types of ships predicted by anaka (98). 8 5 In ig., the result of the thrust force in the same condition is shown. In the calculation, the thrust by the waterjets is assumed to be in forward mode only. At very low speed, more flexible maneuvering performance can be obtained by using reverse thrust mode. In ig.3, the critical value of the K value of Incat m PC is shown with those of two mono-hull ships which were obtained by anaka et al (98). he results suggest that sailing performance of Incat m PC is slightly worse in whole wind direction than a PCC which has similar maneuvering problems in wind. his may be because of its larger superstructure and smaller underwater hulls of the light ship. 3. AIO KEEPIG PEOMACE he station keeping ability in strong wind is important for berthing of a ship. he station keeping ability can be calculated by solving the equilibrium of the forces and moment due to wind with those generated by waterjet thrust forces by systematically changing the thrust and its direction of the waterjet. In the calculation, the experimental wind force and moment obtained in the present study are used. he helm angle of the steering nozzles of the waterjet is changed within ±3 degrees, and the direction of the thrust is changed in forward and reverse modes. he thrust of reverse mode is assumed to be 8% of the normal forward thrust mode. he results of station keeping criteria are shown in ig.4. he lines show the maximum wind speed in m/s and direction during which Incat m PC can be expected to maintain its station, under its own power, without any drift and yaw movement for, 8 and 5% of the maximum thrust force ( tons) by the four waterjets, respectively. In head wind, Incat m PC can stay in up to 87m/s wind, and in following wind in up to 57m/s wind speed. he minimum wind speed of 7m/s appears when wind direction is near 6 for the % thrust. ollow wind ig.4 tation keeping plot of Incat m PC in wind. 4. COCLUIO In the present study, maneuvering performances of a high-speed catamaran in wave-piecing type, Incat m PC are experimentally investigated. ollowing conclusions are obtained. () he wind forces acting on the catamaran are measured and the characteristics of the coefficients are clarified. () he drift resistance coefficient of the catamaran is also obtained by measuring the drifting speed of the model due to wind in a towing tank. (3) Using the experimental data, the criterion of wind speed for straight sailing at a constant speed in wind is calculated. (4) A criterion of wind speed for station keeping in wind is calculated. (5) Maneuvering performances in wind of Incat m PC are revealed. ACKOLEDGME he authors would like to express their appreciation to igashi-nihon hip management Ltd and ICA asmania Ltd for their supplying the technical information on the Incat m PC. hey would like to express their appreciation to Associate Professor. Katayama of Osaka Prefecture Univ. for his help in the experiments. EEECE ) asumi,.(999). Maneuverability of a igh-peed Catamaran unning at Low peed in trong ind, 4 th Japan-Korea Joint orkshop on hip & Marine ession A 87
ydrodynamics. ) ujiwara,.(6). Influence of ave and ind on avigation of PCC, Proc. of PCC PCC ymposium, Japan ociety of aval Architects and Ocean Engineers (Kansai branch) 3) anaka, A. et al. (98). he hip Maneuverability in trong ind, J. Kansai ociety of aval Architects of Japan, vol.76 4) ezaki,.(98). Effect of the ind orce to the peed of a Car Carrier, J. Kansai ociety of aval Architects of Japan, vol.79 5) Inoue,. et al. (97). he Effect of ind on he hip Maneuverability (Ⅰ), J. of est Japan ociety of aval Architects, vol.45 6) Okada, M.(998). A tudy on Assessment of Performances of a ast erry., hesis of undergraduate research project of Osaka Prefecture Univ. ession A 88