Analysis of Duplex Yoke Mooring System for Tandem Offloading of LNG

Transcription

1 Proceeding of OMAE5 4th International Conference on Offhore Mechanic and Arctic Engineering June 7, 5, Halkidiki, Greece OMAE5-679 Analyi of Duplex Yoke Mooring Sytem for Tandem Offloading of LNG Yonghui (Allen) Liu and L. Terry Boatman FMC Technology Energy Sytem SOFEC Floating Sytem 474 Yorktown Plaza Dr. Houton, TX 774, USA ABSTRACT The technology for tranferring LNG between two floating veel offhore i a crucial component in floating LNG facilitie now in the planning tage. A duplex yoke mooring ytem and conventional boom-to-tanker LNG offloading arm were recently developed to carry out tandem offloading of LNG in open ea area with ignificant wave height up to 5.5 meter. Thi paper will preent a methodology to evaluate the operability of the LNG offloading in evere environment. The relative motion between the FPSO and the carrier were predicted by a freuency-domain method. A erie of model tet have been carried out. A good agreement between the prediction and meaurement ha verified and validated the analyi method and procedure. Berthing operation in eatate with a ignificant wave height of 3.5 meter were alo conducted uccefully. Therefore, it can be concluded that the technology of the duplex yoke mooring and boom-to-tanker loading arm i ready to be implemented for a afe and reliable tranfer of LNG in harh open ea environment for LNG facilitie. Keyword: Tandem offloading, LNG, FPSO, Duplex Yoke Mooring. INTRODUCTION Floating production, torage and offloading liuefied natural ga (LNG) facilitie are being evaluated by the indutry to meet the growing energy demand worldwide for environmental friendly, clean-burning LNG. Offhore tranfer of LNG from one veel to another in open ea and poible harh environment i a technical and operational challenge, but ide-by-ide (SBS) tranfer of liuid hydrocarbon and minu 48C liuefied petroleum ga (LPG) i commonplace and i a proven practice in mild environment. Alo well known i tandem (one veel directly behind the other) tranfer of oil through floating hoe ytem for floating production ytem to oil tanker. However, tranferring LNG at minu 6 C between two veel i not common, and ha not been done at all in a production capacity in any evere weather location. SBS tranfer of LNG with conventional loading arm ha been propoed and tudied for many year; and model teting and full ize loading arm teting have been performed by FMC Loading Sytem to prove thoe ytem are atifactory for moderate environment [-3]. Veel motion i the limiting factor in the everity of environment that thee ytem can uccefully operate in, epecially during the flange connection phae of the operation. One example of an expoed weather LNG terminal facility that experience fairly contant wave freuency veel motion i the Shell Brunei loading terminal []. Thi i a facility about 3km offhore, located on a etty without a breakwater, where LNG wa originally tranferred through a tandem loading ytem coniting of multiple degree-offreedom flexing LNG piping arrangement connected with cryogenic wivel oint. The original loading ytem erved for over twenty year. The facility now operate with conventional FMC loading arm that utilize contant motion cryogenic wivel oint to load LNG. The technology for tranferring LNG between two floating veel i a crucial component in floating LNG facilitie. One of the primary application for thi technology i the floating hydrocarbon production unit for field development where large uantitie of ga are preent. Unfortunately, many of the larget offhore ga field are ituated in area of unfavorable weather, Copyright 5 by ASME

2 uch a in the Timor Sea and offhore South Africa. The conventional ide-by-ide offloading with loading arm i limited by the eatate in which it can be operated. A ignificant downtime may be reulted in due to high freuency LNG offloading reuirement. There are ome in the indutry that conider offhore LNG tranfer technology to be a blocking technology, or at leat one more hindrance to the progre of ome maor LNG proect. Although the general weather condition at ome promiing offhore Wet Africa location are not evere, a peritent ea well i expected to caue undeirable veel roll motion during LNG loading. An LNG tranfer ytem that provide maximum operational availability and afety i needed a a part of commercial utification of everal LNG production proect. Berthing an LNG carrier to another floating veel, and remaining moored there for to 4 hour will reuire perfected berthing procedure and robut dependable euipment. A erie of development by FMC Energy Sytem in the evolution of tandem veel berthing and LNG tranfer euipment ha led to the ytem decribed in [], a ytem ideally uited for environment uch a Wet Africa and other location where a tandem LNG tranfer ytem i the preferred olution. The duplex yoke mooring ytem and conventional boom-to-tanker LNG offloading arm were recently developed to carry out tandem offloading of LNG offhore with higher ea tate, up to 5.5 meter ignificant wave height. The duplex yoke mooring ytem conit of a mooring yoke aembly with duplex axe and heavy weight. The mooring yoke aembly connect the bow of the carrier to the tern of the FPSO by two pendant linkage and allow the carrier to weathervane around the bow. The LNG will be tranferred from the tern of the FPSO to the bow of the carrier with the boom-to-tanker (BTT) LNG loading arm. Marine loading arm for handling LNG have been upplied by FMC Loading Sytem for forty year. FMC SOFEC ha provided offhore veel mooring ytem for over thirty year. Through thi experience, an LNG offloading ytem uing proven component from thee two related technologie provide for LNG tranfer rate up to 5, m3 LNG/hr in evere eatate. The new tandem mooring arrangement provide increaed veel afety and higher availability through increaed veel eparation and by the method of berthing the LNG carrier. Improved economic are achieved by the reduced need for large tug auxiliary veel, and alo by the reduced need for thruter and DP control on the LNG carrier. Concept for tandem offloading of LNG have been in development for over ten year by FMC Loading Sytem. Model bain teting ha been done in indutry JIP tudie [3]. A large-cale working model ha been teted uing veel motion data from the model bain tet. The new yoke ytem that utilize a duplex mooring yoke ha been model bain teted for operation in harh offhore environment. The analyi of the tandem offloading ytem i very complex and challenging. There i no exiting oftware capable of evaluating the two body motion accurately with a yoke mooring ytem due to the difficulty aociated with the hydrodynamic interaction and wind and current diturbance between two bodie. The duplex yoke mooring between the two veel make it even more complicated. Thi paper will preent a practical methodology to evaluate the operability of the LNG offloading in evere environment. The relative motion between FPSO and carrier were predicted by a freuencydomain method. A erie of model tet have been carried out. A good agreement between the prediction and meaurement ha verified and validated the analyi method and procedure. Berthing operation in eatate with a ignificant wave height of 3.5 meter were alo conducted uccefully. Therefore, it can be concluded that the technology of the duplex yoke mooring and boom-to-tanker loading arm i ready to be implemented for a afe and reliable tandem offloading of LNG in harh open ea environment for LNG production proect. DEVELOPING LNG TANDEM OFFLOADING SYSTEM The Shell Brunei LNG facility wa the firt boom-to-tanker ytem, and operated uccefully for over twenty year. Although thi loading ytem wa mounted at the end of a etty, not on a floating veel, the ytem wa reuired to connect with a moving veel and load LNG while the veel underwent wave freuency motion in it pread mooring. See Figure. Figure Shell Brunei LNG Loading Facility All of the propoed BTT hip-to-hip LNG tranfer ytem utilize the piping pantograph a the flexible piping component that allow relative motion between the veel. Contant motion cryogenic wivel oint and tainle teel pipe provide all reuired degree of freedom of motion. Figure illutrate the original BTT ytem concept. A carrier connection manifold ytem i reuired on the bow of each LNG carrier. Becaue the ytem ued a nylon hawer to connect the veel, large way motion of the carrier reuired the crane boom to follow the Copyright 5 by ASME

3 motion of the carrier bow manifold. Otherwie the manifold travel could over-reach the phyical limit of the pantograph, epecially when combined with ignificant vertical motion. Motion Envelope Duplex Yoke Conventional Yoke Hawer Mooring Figure 3 Motion Envelope at LNG Carrier Manifold Figure BTT for LNG FPSO Three method have been evaluated for berthing, or connecting, the LNG carrier to the LNG FPSO, ee Figure 3. The original BTT ytem concept ued a nylon hawer to connect the veel, but thi method ha little reitance for ideto-ide motion, and wa limited to moderate ea tate. A conventional oft yoke ytem wa evaluated and found to allow about 36% of the hawer moored veel motion, till exceive unle the pantograph boom follow the LNG carrier motion. A new yoke concept, the duplex yoke wa developed to further minimize the lateral relative motion between the two veel []. The LNG FPSO i ecured to the eabed by an external or an internal turret ingle point mooring ytem, wherea a LNG carrier i connected to the tern of the FPSO by a duplex yoke tandem mooring ytem, which conit of a heavy ballat weight, linkage arm and a yoke a illutrated in Figure 4 and 5. The dual axe are euipped on the top and bottom of the weight. The mooring yoke aembly connect the bow of the carrier to the tern of the FPSO by two pendant linkage and allow the carrier to weathervane around the bow. The LNG will be tranferred from the tern of the FPSO to the bow of the carrier with the boom-to-tanker LNG loading arm. Thi made it poible to keep the pantograph upport boom tationary with repect to the FPSO becaue of the ignificant retriction of the relative motion between the FPSO and carrier by the duplex yoke mooring. For comparion, and with all other variable eual, the lateral motion allowed by the duplex yoke i only about ±.5m relative to the FPSO. Figure 3 how an illutration of comparative motion between the three method. Figure 4 Revolving Boom Tandem Loading Sytem The latet evolution of the revolving boom tandem offloading ytem i illutrated in Figure 4, 5, and 6. Thi concept retain the advantage of the tationary boom when in operation, that advantage being the boom doe not follow the motion of the LNG carrier. In thi cae, the boom i locked in the outboard poition and doe not rotate while loading LNG. The rugged box contruction of the boom afely allow for all reuired roll motion and ide load applied to the piping pantograph. However, the boom can be raied or lowered ± 4.5 meter to allow for large variation in draft of the two veel. Figure 5 Revolving Boom Tandem Offloading Sytem 3 Copyright 5 by ASME

4 FPSO and a huttle tanker, we believe thi aumption will lead to reaonable good reult ince the ditance between two bodie are uite big, typically lager than 7 meter. Figure 6 Tandem Sytem in Parked Poition When the ytem i not loading an LNG carrier, the boom can be revolved around 8 to ecure the boom onto a boom-ret. Then all neceary inpection and maintenance work i readily done on board the FPSO, a illutrated in Figure 6. Concept improvement over the tationary boom concept include the following advantage: There are 6m (3%) added clearance between the two veel Between veel perpendicular meaure 75 meter The overall height of the tructure above waterline i reduced m (5%) The boom height i adutable ± 4.5 m, to provide for large variable draft difference between the two veel Boom wing 8 to park piping pantograph onto ervice platform for improved afety and ervice acce Becaue of the outboard location of the boom wing bearing, no additional deck pace i reuired over the pace previouly needed for the tationary boom concept. THEORETICAL ASSUMPTIONS AND SOLUTIONS To analyze the tandem offloading ytem motion and repone in random wave i very complex and challenge. There i no exiting oftware capable of evaluating the two body motion accurately with a duplex yoke mooring ytem due to the difficulty aociated with the hydrodynamic interaction and wind and current diturbance between two bodie. The duplex yoke mooring between the two veel make it even more complicated. Therefore, we made ome baic aumption to implify the problem and try to find practical engineering olution. The aumption i that the phae difference between motion of two veel would be evaluated baed on the mean ditance between the FPSO and LNG carrier and their yaw angle. The FLNG FPSO and carrier are then analyzed a a eparated obect and coupled with the phae difference. Baed on our experience with tandem offloading arrangement of a The maor limitation of the aumption are that the interaction between two bodie and the FPSO hielding effect on the carrier are ignored. However, thi will reult in omewhat conervative reult for collinear cae, ince the hielding intend to reduce the trength of the wind, current and wave acting on the huttle tanker. Since the hielding effect on the carrier are le important in croed cae than the collinear cae, the accuracy of the prediction hould be good for the croed cae. The maor benefit of the aumption i that the problem can be implified to a ingle body motion analyi and ue the exiting proven technologie for deign and analyi of the duplex yoke mooring ytem for LNG tandem offloading. Therefore, we can analyze the veel global repone with mooring ytem in freuency domain, including the t and nd-order wave exciting force and moment. For the dynamic analyi of the tower yoke mooring ytem we utilized the reult of our in-houe tate-of-the-art computer program SOFTYOKE TM. Thi computer program imulate the highly nonlinear dynamic of a tower yoke moored veel with tower, yoke, ballat and pendant. It ha been deigned to provide a complete, wave-bain-type imulation. It provide detailed tower yoke performance data for a particular veel/mooring combination under pecified water depth and environmental condition. Phyical tower yoke characteritic, including geometric dimenion, ballat weight and hydrodynamic propertie of each element, can be pecified. The mooring load calculation i fully dynamic and utilize a proprietary algorithm for the fat and efficient calculation of nonlinear dynamic load. Long-period ocillation of the ytem are alo characterized and contribution to long-period motion from low-freuency component of variable wind and wave-drift force are computed. The imulation comprie three ditinct phae of calculation: "Static", "low-freuency" (typical period of ocillation of one to four minute) and "highfreuency" or "wave-freuency" (typical period of ocillation of 3 to econd). Wind and current coefficient ued in the analyi are baed on the Oil Companie International Marine Forum (OCIMF) Prediction of Wind and Current Load On VLCC', 994. Wave-drift force coefficient are computed uing a proprietary analytical model (Seaoft). Utilizing the aforementioned coefficient, SOFTYOKE TM determine the mean offet and orientation of the veel and the mean wind, wave and current load acting on the veel, which are all reported in a tatic euilibrium ummary. After the mean load and veel offet have been determined, a low-freuency dynamic analyi i then performed about the mean condition. Thi phae of the analyi take into account the aumed veel characteritic, mooring ytem compoition and environmental condition in the calculation of ytem damping and lowfreuency motion for urge, way and yaw. Baed on the low- 4 Copyright 5 by ASME

5 B B freuency analyi of urge, way and yaw, the ignificant, maximum and minimum pendant tenion and tower load are developed. φ( ) G( p, ) c( p) φ ( p) [ G(, ) ( ) ] ds 4 p φ π S B n n () Having computed ytem mean and low-freuency motion and load, the final phae of the analyi involve computation of wave-freuency induced motion and load. In the computation of wave-freuency mooring load, both uai-tatic loading (which are a function of tatic force-deflection propertie) and nonlinear dynamic loading are accounted for. For the pendant and tower in the ytem, wave-freuency load are computed at it mean plu ignificant low-freuency offet or mean plu maximum low-freuency offet. For each deign cae, component load and motion reulting from the computer analyi are typically combined uing one or more of two method: ) Mean + <Sig> Low Freuency + <Max> Wave Freuency ) Mean + <Max> Low Freuency + <Sig> Wave Freuency Thee are recommended by the American Petroleum Intitute (API). In eence, API ugget that both thee method be carried out to determine which produce the mot evere motion and load in order to have a conervative reult. Method ) precribe that total motion and load be determined by umming the mean ytem value impoed by the environment with the ignificant low-freuency ytem value, and then adding maximum wave-freuency value which have been determined around the ignificant low-freuency value. Thi method i normally ued when wave-freuency motion and force dominate. Method ) precribe that total motion and load be determined by umming the mean ytem value impoed by the environment with the maximum low-freuency ytem value and then adding ignificant wave-freuency value which have been determined around the maximum lowfreuency value. Thi method i normally ued when lowfreuency motion and force dominate. For the purpoe of the preent deign effort, maximum pendant tenion and tower aembly global deign load have been conervatively determined by the above method. HIGHER-ORDER BOUNDARY ELEMENT METHOD In order to evaluate the firt- and econd-order wave excitation on the veel, the higher-order boundary element method (HOBEM) will be utilized to olve the threedimenional potential theory [4-9], which will be briefly decribe here. Only the firt-order wave-freuency problem will be dicued here. The ue of Green theorem with φ and the free-urface Green function G lead to the following integral euation []: where p and repreent field and ource point vector, repectively, and c(p) i a normalized olid angle at point p on the boundary urface S B. B Employing higher-order ioparametric element, the body urface, velocity potential and it normal derivative can be expreed by the higher-order hape function on each element: [ x, y, z] N ( ξ, η)[ x φ( ) φ( ) N ( ξ, η) φ, N n where φ and ( φ n ), y, z ] φ ( ξ, η)( ) n are the value at the -th node and () (3) denote the number of the node on each element. For intance, the hape function for a uadrilateral uadratic element with 8- node can be expreed a (Zienkiewicz [], 977): ( + ξ ξ)( + η η)( + ξ ξ + η η) N 4 ( ξ, η) ( + ξ ξ + η η)[ ( η ξ) ( ξ η) ],3,5,7,4,6,8 Upon dicretizing the body urface S B with M higher-order element and ubtituting E. (3) and (4) in to E. (), we obtain the following algebraic euation for the unknown φk: NOD where, H φ NOD ik φ k Dik i n k H D ik ik M e M e δ Hˆ kr δ Dˆ kr ( e) i ( e) i + c δ i,,..., NOD and NOD i the total number of node on the body urface S B. In E. (6) and (7), δkr denote Kronecker delta and rnenn(,e) i a connective matrix, which repreent the correpondence between the local and global node. ˆ ( e ) H i ˆ ( e ) D i The function and are given by: ik (4) (5) (6) (7) 5 Copyright 5 by ASME

6 Hˆ Dˆ ( e) i ( e) i 4π 4π Γe Γe G( p, ) N dγ n G( p, ) N dγ (8) (9) where N i the -th hape function and Γ e the urface of each element. The full decription about the HOBEM and the formulae for evaluation of the firt- and econd-order wave force can be found in Liu, et al [5-8, ]. The capacitie of the LNG FPSO and carrier were choen a 4,m 3 and 4,m 3, repectively for the tudy. In order to validate the new LNG tandem offloading concept and verify the numerical procedure preented in the paper, a erie of model tet have been conducted for LNG tandem offloading with the duplex yoke mooring ytem in the environmental condition ummarized in Table. The model tet were carried out baed on the cale of :64 and the three-hour torm in prototype were modeled. The procedure of berthing the LNG carrier to the LNG FPSO were alo carried out for the berthing eatate. The tet et-up are hown in Figure 7 and 8. NUMERICAL AND MODEL TEST RESULTS The tandem mooring hall be deigned uch that the integrity of the pantograph ytem i intact in any deign condition. Therefore, tandem offloading deign criteria are The maximum allowable operating motion envelope of pantograph (relative motion between huttle tanker & FPSO) in the maximum offloading torm i le than meter LNG hall be offloaded to a carrier in evere torm The Connection/diconnection of the Carrier can be carried out in eatate up to ninety plu percent of probability of occurrence The mot offhore ga field in the world are located in the area with moderate environmental condition, uch a Indoneia, Malayia, Perian Gulf and Wet Africa. Therefore, the maximum deign condition were choen a the ignificant wave height of 5.5 meter. The wind and current were aumed to be at 45 and 9 degree to the wave for the croed cae. Thee deign condition are very cloe to the one ued for the LNG Offloading JIP by FMC Loading Sytem in 999 [3]. Actually, the 5.5 m wave are relatively evere for mot geographical area. The wave only cae wa choen in order to eliminate any uncertainty aociated with wind and current for a better correlation tudy with theoretical value. We alo varied the peak period of the wave from.5 to econd for the croed cae to ee enitivity of the ytem repone. The environmental condition for the tudy are lited in Table. Figure 7 LNG tandem offloading model tet Table Storm Environment for LNG Offloading Maximum Offloading Seatate Berthing Cumulative Probability % 99.4% Wave Only Croed Croed Croed Water Depth m Wave tral Model P-M P-M P-M P-M Significant Wave Height m Peak Period ec Direction deg Wind Velocity knot Wind Spectral Model API API API Direction deg Current Velocity knot Direction deg Figure 8 LNG carrier berthing operation tet For the wave only cae, the relative motion between the upper cardanic aembly on the LNG FPSO and the lower cardanic aembly on the LNG carrier (ee Fig..) were calculated baed on the aforementioned method and procedure and the predicted reult were found to be more conervative 6 Copyright 5 by ASME

7 than the meaured one a expected, ince the hielding of the FPSO on the carrier wa not conidered in the analyi. The meaured way motion are mainly induced by the fihtailing of the carrier, which i not modeled. For the croed and cae, good correlation between the model tet reult and prediction are oberved. Since the broad ide of both FPSO and carrier are expoed to the wind, wave and current, the hielding effect of the FPSO on the carrier i limited. Thu the calculated low-freuency relative urge motion are lightly le than the tet reult. However, the relative way motion are in better agreement. Particularly, the reultant relative xy motion, the motion envelope are le than the targeted deign value of meter. They match well with the prediction. The meaured ignificant relative vertical motion are in good agreement with the theoretical value a well. The meaured and predicted reultant xyz motion are almot identical. The relative motion between the LNG FPSO and carrier are ummarized in Table. The relative x, y and z wave-freuency motion RAO between the upper cardanic aembly on the LNG FPSO and the lower cardanic aembly on the LNG carrier (ee Fig. ) are preented in Figure 9 and. They are in very good agreement with our prediction. The berthing operation tet were alo performed uccefully in the connection eatate with the ignificant wave height of 3.5 meter a preented in Table. The meaured and predicted maximum hawer tenion are 65 and 6 metric ton, repectively. CONCLUSIONS Therefore, it can be concluded that the feaibility of the duplex yoke mooring ytem for LNG tandem offloading in open ea with ignificant wave height up to 5.5 meter ha been confirmed. The tandem offloading ytem with the duplex yoke mooring ytem i robut and dependable euipment for the LNG tranfer. The theoretical aumption and prediction are verified and validated with good accuracy by the model tet reult. It i atifactory that the implified method propoed in the paper can generate reaonable good engineering approximation to uch a complex problem. The model tet alo confirmed the berthing operation procedure uccefully. Thu, the technology of the duplex yoke mooring and boom-totanker loading arm i ready to be implemented for a afe and reliable tranfer of LNG in harh open ea environment for LNG facilitie. In the future, it i deired to develop a coupled analyi of multi-body motion with duplex yoke tandem offloading mooring ytem and time-domain analyi tool. It i alo expected to conduct extenive model tet with different capacitie of the LNG FPSO and carrier and different combination of environmental condition for a future LNG proect. Table Relative Motion Between LNG FPSO and Carrier ENVIRONMENT Veel Motion and Acceleration Theory Tet Theory Tet Theory Tet Wave Only Croed Croed Surge Downtream mean m tdv. LF m max/min LF m ig WF m Total m Surge Uptream Total m Sway mean m tdv. LF m max/min LF m ig WF m min m max m Heave ig m max m xy max m xyz max m REFERENCE [] Boatman, L. Terry and Mitchell, William B., 4, LNG TANDEM OFFLOADING SYSTEM, Proc. AIChE 4. [] Bliault, A., Reinen, D., Runbalk, D. and Nagelvoot, R.K.,, Shell Floating LNG Plant for the t Century, IGU World Ga Congre, Nice, France. [3] FMC Offhore LNG Loading Sytem JIP Phae I Development Report, 999. [4] Liu, Yong Hui, 988, Analyi of fluid-tructure interaction by uing higher-order boundary element in potential problem and it application in coupling vibration of bending and torion of hip, PH. D. Diertation, Shanghai Jiao Tong Univerity, China, January 988. [5] Liu, Y. H., Kim, C.H. and Lu, X.S., 99, Comparion of Higher Order Boundary Element and Contant Panel Method for Hydrodynamic Loading, Int. J. Offhore and Polar Engineering.,, n., pp. 8-7 [6] Liu, Y. H., Kim, C.H., Kim, M.H. and Boo, S.Y., 99, Second-order Mean Drift Force and Moment on ISSC Tenion Leg Platform in uni- and multi-directional random Sea, Proc. ISOPE'9 [7] Liu, Y. H., Kim, C.H. and Kim, M.H., 993, The Computation of Mean Drift Force and Wave Run-up by HOBEM, Int. J. Offhore and Polar Engineering., 3, n., pp. -6 [8] Liu, Y. H., Kim, C.H. and Kim, M.H., 993, Doublefreuency wave load on a complaint TLP, Proc. of ISOPE'93 [9] Liu, Y. H., Kim, C.H. and Kim, M.H., 994, Time domain imulation of a Tenion-Leg Platform in random ea, ISOPE'94 [] Ogilvie, T.F., 983, Second-order hydrodynamic effect on ocean platform, Intl. Workhop Ship and Platform Motion, Berkeley. [] Zienkiewicz, O.C., 977, Finite Element Method, McGrew-Hill. 7 Copyright 5 by ASME

8 Relative X Rao C, Wave Only Tp Relative X Rao Cr, Tp Tet HOBEM Tet HOBEM 5. X Rao (m/m) X Rao (m/m) Fre (Hz) Relative Z Rao C, Wave Only Tp Tet 3 HOBEM Fre (Hz) Relative Y Rao Cr, Tp Tet HOBEM Z Rao (m/m).5 4. Y Rao (m/m) Fre (Hz) Fre (Hz) Figure 9 Relative X and Z-motion RAO in wave only 4 Relative Z Rao Cr, Tp Figure 4 Relative Y-motion RAO in croed- Tet torm HOBEM Z Rao (m/m) Fre (Hz) Figure Relative X, Y and Z-motion RAO in croed- torm 8 Copyright 5 by ASME