3,- Committee 2, ISSC. 4 April 1972, Lyngby) Calculations of Motions and Hydrodynamic Pressures for a Ship in Waves. by 3. Fukuda and H.

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1 I (ni. 972 RCHEF bliotheek van d bouwkunde nische Hogeschoo ibiotheek van de Onderafdetin sbouwkunde 'Sc e Hogeschoo, DOCUMENATE DATUM: 3,- Committee 2, ISSC 4 April 1972, Lyngby) Lab. v. Scheepsbouwkunde Technische Hogeschool Deift i Calculations of Motions and Hydrodynamic Pressures for a Ship in Waves by 3. Fukuda and H. Fujii This note summarizes briefly the results of theoretical calculations on the motions and hydrodynamic pressures induced on a ship in regular waves, which have been carried out as a part of the research works of the research committee "SR 131" by the cooperation with Kyushu University and Mitsubishi Nagasaki Technical Institute. The calculation method is based upon the strip theory described in Refs. [1] and [2]. In the first place, the ship motions in regular waves from different directions are solved by assuming the coupled equations of heaving and pitching motions and those of swaying, yawing and rolling motions. The non-linear roll damping is introduced into the latter coup1ed equations of motion. Secondly the hydrodynamic pressures induce.d on the hull surface are evaluated by using the solutions of heave, pitch, sway, yaw and roll. A series of calculations has been made for the ore carrier "KASAGISAN-MARU" in full loaded condition. Particulars of the ship are given in Tables 1-3, and the main results of calculations are shown in Figs Large pressures are found on the hull surface at the weather side in beam waves and in bow waves. Next to those cases, considerable pressures are found in head waves. Pressures obtained in following waves and in quartering waves are not large. Comparisons between the calculations and model experiments have been performed by Nakarnura at Osaka University for the case in head waves, where the practically good agreemerlts are fouid for both motions and pressures. Model experiments in oblique waves have been continued at the seakeeping model basis o: Tokyo University and of Ship Research Institute, but co'risons between the calculations and experiments are not yet ccotnplished.

2 References [1] J. Fukuda: "Theoretical Evaluations of Transverse Wave Loads" Discussion to the Report of Committee 2, Proceeding of 4th ISSC, Tokyo, (2] J. Fukuda, R. Nagarnoto, M. Konuma and M. Takahashi: "Theoretical Calculations on the Motions, Hull Surface Pressures and Transverse Strength of a Ship in Waves" Journal of the Society of Naval Architects of Japan, Vol. 129, June Nomenclature h0: wave amplitude H(=2h0): wave height X : wave length k (=2ir/A): wave number heading angle L : ship length Fn.: Froude number : heaving amplitude pitching amplitude e0: rolling amplitude Zro: amplitude of ralative motion to the undisturbed wave surfase P0: amplitude of hydrodynamic pressure pg : specific weight of sea water t:time Te: wave encountered period

3 Table 1 Main Particulars Length between Perpendiculars (L) in Breadth Moulded (B0) in Depth Moulded (D) in Draught Moulded (d0) in Displacement (W) 135,666 t Block Coefficient (Cb) Midship Coefficient (Cm) Water Plane Area Coefficient (Cv) Centre of Gravity from Midship (xg) in Center of Gravity below Water Line (ZG) in Metacentric Radius (G0M) in Longitudinal Gyradius (K1) L Transverse Gyradius (Kt) B0 Rolling Period (TR) sec Table 2 Estimation of Roiling Period Density of Ore * 2.70 Occupied Ratio of Hold 100 % 80.5% 65.6 KG in in in GM 2.18 in 4.18 in 5.42 in GG0 (Free Surface Effect) 0.05 in 0.05 in 0.05 in G0M 2.13 in 4.13 in 5.42 in Kt/BO KL/BO TR s s 9.41 s * In this report the density of ore is assumed to be 2.2

4 Table 3 Breadth, Draught and Sectional Area S.S. B/BQ d/d0 S/S0 A.P / / / / / / / / / / F.P k (0.1317)

5 1.5 HEAVE Xz (L:SHIP LENGTH, A: LENGTH) Fig. 2 Heaving Amplitudes in Regular Beam WaVes

6 PITCH X9O Fn:Q I Fig. 3 pitching Amplitudes in Regular Beam Waves

7 Fig. 4 Heaving Amplitudes in Regular Bow Waves

8 RI TCH Y135O /\-I rno cinc LJ.t.JJ IL/A 1.5 Fig. 5 Pitching Amplitudes in Regular Bow Waves

9 1.5 HEAVE X =MO Fti O ,,/ I.-' \\ OJO. a o '1.5. Fig. 6 Heaving 1\mplitucles in Regular Head Waves

10 1.5 1,0 PITCH X O0 Fn0 Q I 'LU 1.5 Fig. 7 Pitching Amplitudes in Regular Head Waves

11 3 ROLL X9O FnO.1O +1w =5 ici 15m (H= 2) c. T : 1.5 -JLI? Fig. 8 Rolling Amp].itudes in Regular Beam Waves

12 0 2 0 T JL/A I- Fig. 9 Rolling Amplitudes in Regular Bow Waves

13 SECTION WEATHER SIDE LEEWARD SIDE HEADING 9Q0 S.S.2- HEIGHT lom MIDSHIP FROUDE NO S.S I I 0 S Fig. 10 Amplitudes of Relative Motion in Regular Beam Waves

14 I S.S. 8 SECTION I. POSITION KEEL CENTRE LINE BILGE WATER LINE WEATHER SIDE LEEWARD SIDE WEATHER SIDE LEEARD SIEE HEADING 900 HEIGHT F ROtJDE NO. lom S.- -,.5, S.---- j.0 7 N SS S L/1s. Flcj. ii Amplitudes of Hydrodynamic Pressure in Regula.r Beam Waves

15 SECTION WEATHER - SIDE S.S.2 MIDSHIp S.S.4 LEEWARD SIDE HEADING. 135 'HEIGHT lom FROUDE NO N 2.0 i o >- Jri1 1.5 Fig. 12 Amplitudes of Relative Motion in Regular Bow Waves

16 s.s. SECTION POSITION HEADING 1350 KEEL CENTRE LINE WEATHER SIDE BILGE LEEWARD SIDE WATER WEATHER SIDE LINE LEEWARD SIDE HEIGHT FROU-DE NO. lom QC : / / / / /1/.,,,- / I' /i7i. Fig. 13 Amplitudes of Hyciroclynamic Pressure in Regular Bow Waves

17 - - S.S.2 SECTION MIDSHIP WEATHER SIDE LEEWARD SIDE HEADING 1800 Tf71-TrT FROUDE lom o.io IL/X Fig.. 14 Amplitudes of Relative Motion in Regular Head Waves

18 S. S.. SECTION POSITION HEADING 1800 KEEL CENTRE LINE WEATHER SIDE BILGE LEEWARD SIDE WATER WEATHER SIDE LINE LEEWARD SIDE - - HEIGHT FROUDE NO. r lom 0.10 i 2.0. i Fig. 15 Amplitudes. of Hydodynamic Pressure in Pegular Head Waves

19 s.s. 4 SECTION C) r-4 P0/pp40 SHIP LENGTH HEIGHT FROUDE NO. 247m 1Cm " i..i_, 'V / Fig. 16 Amplitudes of Hydrodynamic Pressure on the Hull Section in Regular Beam Waves of Different Lengths

20 S.S. 8 SECTION 0 r1 LENGTH - I-I El G I-IT FROUDE NO. loin Fig. 17 Amplitudes of Ilydrodynamic Pressure on the Hull Section in Regular Bow Waves of Different Lengths

21 S.S. 8. SECTION ai1i0 SHIP LENGTH HEIGHT F ROUDE NO. 247rn 1 Om Fig. 18 Amp].itudes of Hydrodynarnic. Pressure on the Hull Section in Regular Head Waves of Different Lengths

22 0 SHIP LENGTH 247m 2,0 1.0 \\\ S.S. 8 SECTION E 0 Po/pgAo 1,0 2O I if /I -I- / 1.00 FROUDE 0.10 NO. 2 0 HEIGHT 5m loin 15m 4_ S Fig. 19 AmplitUdes of ilydrodynamic Pressure on in Regular Bow Waves of Different Heights the 1-lull Section

23 p I SHIP SECTION MOTION AMP. P1-LAS E ' I.L. 10 HEAVE ' PITCH 5rn 4.895' SCALE m ROLL t = T/8 t= 0 t 3T/8 t = Te/4 SURFACE S. W. t-. -. YE--- ui- - t 3Te/4 7Te/8 Fig. 20 Pressure Distributions on the Hull Section during an Encountered Period in Regular Eow Waves