- inertia forces due to the virtual mass of the tanker

OTC 7444 Investigation Into Scale Effects on Motions and Mooring Forces of a Turret-Moored Tanker Johan Wichers and Albert Dercksen, Maritime Research Inst. Netherlands Copyright 1994, Offshore Technology Conference This paper was presented at the 26th Annual OTC In Houston, Texas, U.S.A., 2-5 May 1994. This paper was selected for presentation by the OX: Program Committee following review of information contained In an abstract submitted by the author($). Content$ of the paper. as presented, have not been reviewed by the Offshore Technology Conference and are sub]ed to wrrectlon by the author@). The material, as presented, does not necessarily reflect any posltlon of the Offshore Technology Conference or its officers, Permlssion to wpy Is restricted 10 an abstract of not more than 300 words, Illustrations may not be wpied. The abstract should mntaln wnsplcuous acknowledgment of where and by whom the paper Is presented. ABSTRACT A loaded 200 kdwt tanker moored by means of an internal bow-turret is exposed to survival conditions (colinearly directed irregular waves and wind). The water depth amounts to 82.5 m and the turret mooring system consists of 6 equally spaced chains. By means of time-domain computations of the coupled chain-mooring-tanker system the wave frequency (WF) and low frequency (LF) turret motions and chain/turret forces are simultaneously determined. The model tests were carried out on scale 82.5. The results of the computations are compared with the results of the model tests using the wave registration as calibrated in the basin. The comparison required the modelling of some additional damping which is expected to originate from small sway and yaw motions which were measured during the model test. Investigations on scale effects in the resistance coefficients of the hull in surge direction are presented. Finally the sensitivity to changes in the values of the drag and inertia coefficients of the chains on the mooring loads in the chains and turret construction is given. References, tables and figures at end of paper INTRODUCTION A moored tanker exposed to irregular head seas performs small amplitude WF pitch, heave and surge motions and relatively large amplitude low frequency surge motions around a mean surge displacement. The mean surge displacement is caused by the mean wave drift force and the steady wind force. The low frequency surge motions are due to the low frequency part of the second order wave drift forces. Since the total damping of the low frequency motions is small, and in irregular head seas the frequency of the slowly varying forces corresponds to the natural surge frequency of the system, resonance occurs. Large low frequency surge motions and consequently large mooring forces may be the result. For the design of the mooring system, the large amptitude motions and the corresponding forces are required and it is therefore of prime importance to have knowledge about the low frequency excitation and reaction forces. The excitation and reaction forces as acting on a chain-turret moored tanker are given below: - velocity dependent wave drift forces (including wave drift damping) - viscous damping forces - wind damping forces - inertia forces due to the virtual mass of the tanker - restoring and damping forces caused by the mooring system. In order to determine the total restoring and damping forces of the mooring system the wave frequency tanker motions are required too. By means of an integrated computation (mooring-system-tanker) in the time domain, the instantaneous WF and LF restoring and damping

2 Investigatkn bnu Scale Effects on Motiuns and Moothg Forces of a Turret Moored Tanker OTC7444 forces as acting on the mooring lines and the turret construction will be used as input for the equation of low frequency motion of the tanker at every time interval to solve the new low frequency turret motions and velocities. The contribution of the hydrodynamic damping induced by the mooring chains on the low frequency part of the vessel motions may be considerable as was shown in Refs. [l] and [2]. In this study the still water damping of the hull and mooring system, the wind damping and the wave drift damping were input for the simulations, the influence of the chain damping was incorporated implicitly in the simulations. In previous studies with a tanker exposed to irregular survival head waves a tanker was linearly moored in both longitudinal and transverse direction to prevent possible small low frequency yaw and sway motions, see for instance Refs. [3], [4] and [5]. In the present study the mooring system allows unrestricted yaw motions in combination with relatively small sway motions. In head waves and head wind these motions can be induced by instabilities in the system and disturbances in the wind and wave field. The additional linear damping coefficient related to transverse and rotational motions as observed in the model tests was determined and compared to the pure surge direction. The differences in magnitude between the viscous damping in still water and in current in pure surge direction for both model scale and full scale have been investigated. The results in current show comparable damping values when marine growth is assumed for the full scale case. Finally by means of computations the sensitivity of the values of the drag and inertia coefficients of the chains on the forces in the chains and turret construction is given. From the results it can be concluded that the effect of the chain drag and inertia coefficients on the chain forces and tanker motions are relatively small. MODEL TESTS Descriptkn of the system For the computation and model tests use is made of a loaded 200 kdwt tanker moored by means of an internal bow turret. The particulars of the tanker are given in Table 1. The turret was located 35 m aft of the FP. The chain turntable was at base level. The chain table was connected by means of six equally spaced chains. The test set-up is given in Figure 1. The particulars of the chains are given in Table 2. The water depth amounts to 82.5 m. The static load deflection curve is given in Figure 2. Model tests measurements The model tests were carried out in the Wave and Current basin of MARIN on scale 82.5. The tanker was exposed to P.M.-type wave spectrum with a significant wave height H,=lO m and peak periods of respectively Tp=12.96 S and 15.55 S. A colinearly directed wind was generated by means of a battery of wind fans resulting in a mean wind force of 80. The forces in the six chain legs close to the location of the turntable, the three forces in the turret and the six tanker motions were measured. The measurements started after a transient period of 30 minutes and lasted for three hours full scale. The results of the measurements are scaled according to Froude's law of similitude. Statistical analyses are shown in Tables 3 and 4. In Figures 3 and 4 time registrations of the heaviest loaded chain and the surge motion at the turret are displayed. THEORY Equations of bw frequency tanker motion In order to predict the motions of a moored tanker in irregular head waves and head wind and in combination with its mooring system, the equation of motion for all elements are solved. The equation of low frequency surge motion is given below: in which: M a B X i X 'wind Xwavedrift 'mooring = mass of the tanker added mass of the tanker at the natural surge frequency a linear damping coefficient consisting of still water damping, wind damping and wave drift damping = low frequency surge excursion of the tanker = low frequency surge velocity of the tanker = low frequency surge acceleration of the tanker = wind force ( possibly time dependent ) = time dependent wave drift force = instantaneous restoring force due to the mooring system due to the WF and LF dlsplacements, velocities and accelerations. The added mass of a tanker can be determined relatively straight forward by means of 3-D potential theory at low frequencies. The linear hydrodynamic damping coefficients (still water and wave drift damping) in the left hand side of the equation can be determined from the data given in Ref. [4]. The steady wind force is calculated according to the OClMF formulations. The wind damping is obtained using the formula 2+XWind/vwind.

J.E.W. Wichers and A. Dercksen The wave drift force is calculated by means of a second order impulse response technique using the second order wave drift force transfer function and the wave train as measured in the basin. The mooring force contains basically the static load restoring curve together with a dynamic amplification function which takes care of the wave frequency oscillations of the mooring lines. As a resul of the dynamics in the mooring system an additional damping (and restoring force) is introduced in the system. This damping is very complicated and cannot be modelled as a simple linear damping. It depends on the amplitude and the frequency of the oscillation, as well as the mean tension in the line, the water depth and the mooring line layout. Equatkns of moth for mooring system The mooring system is modelled by means of the lumped mass method, where each anchor line is represented by a large number of discrete elements. For each node j in the discretization the governing equation of motion in a global system of coordinates is the following: where: [Aj] = the inertia matrix [aj(t)] = ji. = time dependent added inertia matrix global acceleration vector $,(t) = nodal force vector (tension, weight, fluid and seabed reaction forces). The fluid forces originate from element motions and water particle motions due to current and waves. The Morison formulation and relative motion concept are applied. Vertical seabed reaction is modelled by a system of linear critical damped springs. Horizontal reaction forces are modelled by means of a Coulomb friction model (friction coefficient Cf = 0.6). A coupled set of non-linear equations is obtained for the nodal positions in time, and the boundary conditions are used to superimpose the WF and LF vessel motions. The mooring reaction force on the turret, caused by the chain legs, is updated at each time step. Due to the importance of the high frequency chain dynamics, the simulation technique is essentially in the wave frequency range, but time steps may be as small as 0.025 seconds. Computational approach The computational procedure consists of two stages, i.e. preparation of input followed by a simulation in the time domain. The input preparation consists of: - generation of a wave drift force time history based on the second order wave drift transfer function and a wave registration; - generation of high frequency turret surge and heave motions based on the tanker RAO's and a wave registration; - discretization of the mooring system; - input of the mean wind force, still water damping, wave drift damping, wind damping and possible additional damping contributions. The time-domain simulation comprises two basic steps: - solve the equation of low frequency surge motion for the tanker, using the mooring force from the previous time step in the high frequency time scale; - add the high frequency turret motions to the actual tanker position, update the mooring forces and proceed with the first step. DISCUSSION OF RESULTS Verification runs The simulations which were carried out to compare with the model test results are presented in Tables 3 and 4 and Figures 3 and 4. As can be seen, the agreement with the model tests is good. The tanker excursions and mooring loads are well predicted. In order to obtain these results, an additional damping was used in the simulations. Based on a comparison with a low frequency simulation using the same drift force registration it was also possible to estimate the approximate contribution of the chain damping as a linear damping term. The following damping factors were determined: 61 B1 l 31 20 28 20 stm slm Bl W 5 5 sfm 'tchain 30 10 stm Baddi~onal 40 30 sfm -------m Bb&~ 126 93 slm in which: B1 = wave drift damping P B1 1 still water damping derived from data given in Figure 6 Bl = W wind damping based on wind force S 'lchain estimated chain damping Baddibnal P additional damping from model test

4 Investigation MO Scale Effects on Motions and Mowing Forces of a Turret Moored Tanker OTC7444 As can be seen for both spectra the additional damping is 32% of the total damping. The origin of this additional damping term is assumed to be caused by the fact that the tanker experienced small yaw and sway motions during the model test. In order to take this effect into account the simulations should be carried out with the complete equations of motion comprising the coupled equations in the surge, sway and yaw mode of motions. At present the complete simulation procedure is under study. The damping is an important input for the determination of the low frequency motions and mooring forces. In order to understand the full scale values some investigations have been carried out on the scale effects of the damping. Because the wave drift damping originates from potential theory (Ref. [4]), no scale effects will occur. Since the wind damping is obtained from the applied wind force (OCIMF) no scale effects are involved. The still water and chain damping, however, are from viscous origin and scale effect can occur. In the following these scale effects are discussed. Scale effects: surgo damping h current on tanker hull In order to investigate scale effects on the tanker hull in surge direction, first the tanker in steady current is considered. To study the scale effects use can be made of the ITTC-line or the well-known Schoenherr Mean Line as given'in Figure 5. By means of the Reynolds number the friction coefficient Cif on a flat plate can be determined. The resistance force on a ship hull can be calculated as follows: in which: C,, = friction coefficient k S form factor (ship and Reynolds number dependent, varies between 0.0 and 0.5) p = specific density of seawater ( 0.1045 s2/m4) S = wetted surface V, P current velocity in m/s For Reynolds numbers on model scale and full scale the friction forces have been determined for a flat plate (k=o). The results are given in Table 5. Further the MARIN computer program PARNASSOS (PARabolised NAvier-Stokes Solution System) has been used to compute, on model scale, for both the turbulent and the laminar flow, the viscous resistance on the 3- dimensional hull form of the 200 kdwt tanker. The computer program is described in Ref. [6]. The results are given in Table 5. In Table 5 the model scale resistance forces have been given for full scale using Froude's law of similitude. In the same table the current forces as measured on the 200 kdwt tanker are also presented. Comparing the computed resistance forces and the results of current measurements it can be concluded that the current flow on model scale can be considered as turbulent and that the computed and measured current loads are of the same order of magnitude. In addition the form factor on model scale as can be derived from ITTC-line results and the PARNASSOS results will be approximately k = 0.29. The resistance forces on the tanker for full scale according to the ITTC-line and the computation of PARNASSOS are given in Table 5. From the results a form factor of approximately k X 0.44 can be derived, and the following conclusion can be drawn: the resistance on full scale is considerably smaller than measured on model scale. When marine growth andlor anode protection on the tanker hull is taken into account, the conclusion above must be revised. The friction coefficients for a roughened plate is given in Figure 5. If the roughness is assumed to be 1 cm the resistance force will become of the same order as measured in model scale (using the same form factor as for a smooth hull). Because the damping is directly related to the resistance force (2*X, JV,), approximately the same damping as measured in the basin can be found. Scale effects: surge damping h still water The above description is applied to an oscillating vessel in surge direction in head current. When there is no current, the body is oscillating in still water. To determine the damping forces on a hull form, distinction can be made in a turbulent and in a laminar flow along the body. Turbulent flo W Myrhaug described in Ref. [7] a model for estimating the frictional forces on an oscillating plate. Huse and Matsumoto (Ref. [B]) apply the same approach for a flat plate in turbulent flow and introduce a form factor., k, to account for the increase in oscillatory viscous forces acting on a tanker. The amplitude of the viscous force component in phase with the surge velocity is: in which: o = surge frequency xi, = surge amplitude

OTC7444 J.E.W. Withers and A. Dercken 5, C,, = friction coefficient fl,(l +k,.) S E wetted surface of the hull 2 4 p = 0.1045.s /m where lw f is the flat plate friction coefficient, which according to the Johnsson formula Ref. [8] for turbulent oscillatory flow is approximately: and the Reynolds number for oscillatory is defined as: in which u 1.l8831 'l 0& m2/s (water temperature of 15 *C) Laminar flow In order to study the laminar case, the theory of an oscillating plate with a laminar boundary layer can be used, see Ref. [g]. In Ref. [4] the derivation of the following formulation for the resistance of a tanker is given: x10,c. = PG S v, cos(; in which: p = 0.1045.s2/m4 o X surge frequency v = 1.1863110'~m~/s S = wetted surface of the hull v, = surge velocity amplitude For model scale and full scale the damping forces for both the turbulent and laminar boundary layer have been calculated. The results are given in Table 6. The results of the measured damping forces are given in Figure 6 also. From decay tests (model scale) with a linearly moored tanker it was found that the viscous damping forces in surge direction were linearly proportional with the surge velocity. By means of model tests with tankers having various dimensions and mooring spring constants the viscous damping coefficients in the surge mode of motion were determined. The results as a function of wetted hull area and surge frequency are given in Figure 6, derived from Ref. [4]. For the 200 kdwt loaded tanker with a natural period of 200 seconds (average period in the time domain simulations, see Figures 3 and 4) a damping coefficient B1 = 20.s/m can be read from Figure 6. It must be noted that all computed and measured values for model scale were transformed to full scale by applying Froude's law of similitude. In Table 6, under the heading model scale, the form factor., k, was determined by relating the computed damping forces to the measured damping forces (B1 = 20.s/m), For the turbulent case the form factor strongly depends on the ReynoMs number. For the laminar case the form factor is constant and amounts to kodc.= 0.55. The magnitude of the form factor is in the same order as found for the current loads. From the results it may be concluded that the results on the computed damping in a laminar condition and the measured damping forces both on model scale give a reasonably good agreement. In Table 6, under the heading prototype, the full scale damping forces for both laminar and turbulent conditions are given. Applying the same form factor as found for the model scale the damping forces for the turbulent condition are approximately a factor 3.75 smaller than determined at model scale. The effect of marine growth and dependency of the form factor on Reynolds number, however, are unknown and more research is required to understand the damping forces for an oscillating tanker in the surge mode of motion in full scale. Scale effects: reaction forces on chains For both wave spectra the following parameters for the chain hydrodynamic coefficients have been varied: -Cdn ~2.2; C = 1.6 Cdt = 0.4; Cit = 1.2 (base case used in comparison with model tests) In Figure 7 see Ref. 1101, chain drag coefficients based on the nominal diameter (defined as the wire diameter of a shackle) for various Reynolds numbers are presented. The value which was used for the verification runs was 2.2. The minimum and maximum values from Figure 7, 1.1 and 3.3 were also used. Similar variations were applied to the normal added mass coefficients for the chains. The results of the computations are given in Tables 7 and 8. Observation of these tables show that the influence of the normal added mass coefficient is very limited. The sensitivity to variations in the chain drag coefficient are more pronounced, however, still a minor effect on the tanker excursions and mooring loads is predicted. For both waves, the resulting variations in the significant values of the horizontal turret motions are approximately 5% as a result of a 50% variation in drag coefficient. For the leading chain tension the variations are approximately 6%.

6 Investigation into Scak Effects on Moth and Moorhg Foms of a Turret Moored Tanker OTC7444 CONCLUSIONS The following conclusions can be drawn from the study: 1. Due to the small amplitude yaw and sway motions of the turret moored tanker in irregular head waves and head wind additional damping was generated. From the results of the computations it can be concluded that an additional damping of 32% of the total damping was necessary. Taking into account the additional damping a good comparison is found between the measured and the computed results. 2. The small amplitude yaw and sway motions as measured during the model tests are assumed to be caused by instabilities of the system and small disturbances in the wave and wind field. For a correct representation of the model tests the 3-dimensional (combined surge, sway and yaw) version of the computer program should be used. 3. The current loads on a tanker on model scale can be reasonably well predicted. On prototype, the resistance forces are considerably smaller than measured on model scale. If marine growth andlor anode protection on the tanker hull is taken into account the resistance force on prototype and model scale may be of the same order of magnitude. 4. The still water damping in surge direction can be reasonably well predicted on model scale by using the laminar flow condition. For full scale the resistance forces appear to be considerably smaller than measured on model scale. The effect of roughness and the dependency of the form factor on the Reynolds number, however, are unknown and more research is required to understand the damping forces on full scale. 5. The effects of variation of the chain drag and inertia coefficients on the motions of the tanker and the forces in the anchor chains are relatively small. REFERENCES 1. Huse, E. and Matsumoto, K. : "Mooring line damping due to first and second order vessel motions", OTC# 6137, Houston, 1989. 2. Wichers, J.E.W. and R.H.M. Huijsmans: "The contribution of hydrodynamic damping induced by mooring chains on low frequency vessel motions", OTC paper# 6218, Houston, 1990. 3. Pinkster, J.A. and J.E.W. Wichers: " The statistical properties of low frequency motions of non-linearly moored tankers", OTC paper# 5457, Houston, 1987. 4. Wichers, J.E.W.: "A simulation model for a single point moored tanker", PhD Thesis, Delft University of Technology, 1988. 5. Wichers, J.E.W.: " Wave drift forces and motion response of moored tankers in bi and multi chromatic waves", 2" Offshore Symposium Design Criteria and Codes, Houston, April 1991. 6. Hoekstra, M. and Raven, H.C.: "Ship boundary layer and wake calculation with a parabolised Navier- Stokes solution system", 4" lnternational Conference on Numerical Ship Hydrodynamics, Washington D.C., 1985. 7. Myrhaug, D: "On the frictional resistance of oscillating rough and smooth surfaces", International Shipbuilding Progress, Vol. 31, No. 360, Aug. f 984, pp. 196-203. 8. Huse, E and K. Matsumoto: "Viscous surgedamping of floating production vessels moored at sea", Proc. OMAE, The Hague, 1989. 9. Lamb, H.: "Hydrodynamics", 6" edition 1932, Cambridge University Press, London. 10. FPS 2000 Mooring and positioning, Report Part 1.5: "Mooring line damping-summary 8 Recommendations", 1992.

OTC7444 J.E.W. Withers and A Dercksen Table 1 Main particulars and stability data of tanker Designation Symbol Unit Value Length between perpendiculars LP P m 310.0 Breadth B m 47.1 7 Depth D m 29.7 Draft ( even keel ) T m 18.9 Wetted area S m 22,804 Displacement volume V m3 234,994 Centre of gravity above base KG m 13.7 Centre of buoyancy aft FP LCB m 148.3 Metacentric height GM m 5.78 Longitudinal radius of gyration ky Y m 74.5 Transverse radius of gyration kxx m 16.1 Virtual mass tanker m,.s2/m 26,147 Table 2 Main particulars of mooring arrangement Designation Symbol Unit Value Number of chains 6 Chain diameter Length of each chain Chain table diameter Chain mass in air Weight in air Chain weight in water Longitudinal stiffness Pre-tension angle Pre-tension Chain table above sea bottom inch m m kgfs2/m2 kgflm kgflm deg m

Table 3 Measured and computed resuls l,,= 12.96 S, H, = 10 m (ind. pre-tension) Table 4 Measured and comp (incl. pre-tension) TEST NO. 902701 TEST NO. 902603 NOTATION DIlQMSION HEAN ST. DBV. A IRX. + A m. -...... NOTATION D-SION M... X TURRET [m] Y TURRGT [m1 Z TURRET [m1 ROLL TAUK [dog1 PITCH TANK [dog] YAW TANK [deg] FX TURRET FY TURRET F2 TURRET [t f [J [] Fchain 1 Fchain 2 [ l [ 1 Fchain 3 [ 1 Fchain 4 [ 1 Fchain 5 [ 1 Fchain 6 [ 1 --- Computations --- X TURRET [m1 ZTURR~LT [m1 ROLL TANK [d-l PITCH TANK [dog] YAW TANK [degl FXTURRET [l FY TURRBT [] FZ TURRET [l Fchain 1 [ 1 Fchain 2 i 1 Fchain 3 Fchain 4 [ 1 [l Fchain 5 [ 1 Fchain 6 [ 1 X TURRET [m] z TURRXT [m1 PXTURRBT PI TURRET [] [ t f l Fchain l Fchain 4 [ 1 [ 1 Fchain 1 Fchain 4.[ l c l

J.E.W. Wichers and A. Dercksen Table S Current forces Model scale "c "m R fl m lltc Turbulent PARNASSOS Laminar Measured') mls m's Xlf X1 f k Xlf Xlf 0.77 0.085 2.69E5 4.5 5.75 0.28 1.09 6.0 1.545 0.1699 5.38E5 15.33 19.83 0.29 8.05 24.1 2.32 0.2549 8.07E5 31.52 40.76 0.29 25.58 54.36 ') Based on average current coefficient from measurements Prototvoe Table 6 Still water damping forces Model scale *I a X~am am Rnw,m fiwm 4 am Calc. turbulent Xi -C. Calc. larninar Meas. m 16 m 0.194 rad/s 0.2853 9036 0.01456 mls 0.0553 4.49 (k~.) 1.24 6.49 (km.] 0.55 10.05 8 0.096 0.2853 2213 0.0193 0.0274 1.48 2.96 3.25 0.55 4.98 4 0.048 0.2853 553 0.0255 0.0137 0.49 4.08 1.62 0.55 2.49 *) Based on (l +k,.)

Table 7 Effect of Cdn and Cin values on the chain forces Tp = 12.96 S, HS = 10 m (Run duration 1 hour full scale, using the same synthetic wave train) Table 8 Effect of Cdn and Cin Tp = 15.55 S, H, = 10 m using the same synthet ------------------------------------------------------------------ NOTATION DIMENSION MEAN ST. DEV. AMAX. + A M. -... NOTATION DIMENSION MEAN ----_-------------------------- x turret [m] 12.76 5.74 23.62-4.24 FX turret, [l 172.81 131.57 694.99-35.48 FZturret tl 239.02 33.97 366.41 156.89 Fline 4 [ 1 152.03 105.83 610.23 28.53 ------------------------------------------------------------------ X turret [m] 10.87 FXturret [l 175.77 FZ turret [] 239.27 Fline 4 [l 163.66 -------------------------------- X turret [m] 12.75 5.77 23.64-4.40 FX turret [l 172.79 132.17 697.50-36.97 FZ turret [] 239.09 33.95 367.15 155.19 L Fline 4 Il 152.48 106.53 613.47 28.27... X turret [m] 10.89 FXturret [] 175.72 FZ turret [ l 240.17 Fline 4 [l 163.65 --------------------------------- X turret [m] 12.74 5.78 23.64-4.47 FX turret [l 172.79 132.44 696.82-36.88 FZ turret [] 239.03 34.12 368.24 157.23 Fline 4 [l 152.21 106.70 612.15 17.56 ------------------------------------------------------------------ X turret [m] 10.84 FX turret [l 175.77 FZ turret [] 239.53 Fline 4 [l 163.20 --------------------------------- X turret [m] 12.84 FX turret [l 172.47 FZ turret [] 237-86 Fline 4 [l 156.45 X turret [m] 10.88 FXturret fl 175.37 FZ turret [l 237.98 Fline4 [l 169.75 X turret [m] 12.75 FX turret [] 173.15 F2 turret [l 239.41 Fline 4 [] 149.57 X turret [m] 11.00 FX turret I l 175.42 FZ turret [ l 240.61 Fline4 I) 159.40

J.E.W. Withers and A. Dercksen Fig. 1 Layout of test set-up C PX-NRRET'ICALCJ FX-TURREllMUS.l CHAIN 4 FORWCMC.1 Q CHAIN 4 F0RCEfMEAS.I - - - --- CHAIN 3151 FORCEICALC.1 A CHAIN 151 FORCEIMEAS.1 io TURRET EXCURSION W M Fig. 2 Static load-displacement curve of mooring system 245

12 Investigation into Scale Effects on Motbns and Moorhf~ Forces of a Turret Moored Tanker OTC7444

J.E.W. Wichetg and A. De&n Plate with roughness Smooth plate (ITTC) Fig. 5 Resistance on smooth and roughened plate

Tanker size: o 200 kdwt (100% loaded) 250 kdwt (100% loaded) + 55 kdwt ( 80% loaded) o Symmetrical V = 213,717 m 10.0 Cd for circular cyl. ref. Schlichti o Cd, model chain d = 1.05 mm. t x Cd, model chain d = 1.05 mm, w Cd, stud-link chain d = 30 mm, X Cd, stud-link chain d = 30 mm, 0 Cd, stud-link chain d = 65 mm (0 + Cd, stud-link chain d = 65 mm (4 IU P 03 1.5 3.0 2.5 2.0 1.0 v ++ U l 0. h 0 1 2 3 4 5*105 3-1 * s ~ in ' m ~.S Fig. 6 Measured viscous damping coefficient for the surge mode of motion as function of wetted hull area and surge frequency 0.1 1 1 1 1 )U11 1 1 1 11111 I 1 1 1 111 1 1 E2 1 E3 1 Reynolds num Fig. 7 Drag coefficient of chain, refe