An Investigation into the Effects of Roll Gyradius on Experimental Testing and Numerical Simulation: Troubleshooting Emergent Issues

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1 An Investigation into the Effects of Roll Gyradius on Exeriental esting and Nuerical Siulation: roubleshooting Eergent Issues Edward Dawson Maritie Division Defence Science and echnology Organisation DSO-N-140 ABSRAC his reort resents the analyses, results and recoendations of an investigation into the secification and deterination of a latfor's roll radius of gyration and its influence on the easured or redicted roll resonse of a aritie latfor. he investigation and reort seek to resolve known deficiencies in the secification and deterination of roll radius of gyration and rovide direct guidance and suorting inforation to the exerienter and analyst to suort shi otion analysis. hree solution sets were develoed based on the results of the investigation. he solutions include: the establishent of a ethod of secifying roll radius of gyration requireents; the develoent of a decision tree tool to guide the analyst to the aroriate ethod of deterining the roll radius of gyration; and a set of syste level technology solutions that enable the roll radius of gyration to be deterined for odel scale, full scale and virtual aritie latfors. RELEASE LIMIAION Aroved for ublic release

2 Published by Maritie Division DSO Defence Science and echnology Organisation 506 Lorier St Fisherans Bend, Victoria 307 Australia elehone: Fax: (03) Coonwealth of Australia 015 AR January 015 APPROVED FOR PUBLIC RELEASE

3 An Investigation into the Effects of Roll Gyradius on Exeriental esting and Nuerical Siulation: roubleshooting Eergent Issues Executive Suary he nuerical shi otion siulation and analysis tools used by the Defence Science and echnology Organisation (DSO) are an efficient and effective eans to deterine and evaluate the otion erforance of a latfor oerating in a seaway. However, their accuracy and alicability are strongly influenced by the initialisation data inut by the user. he use of incorrect data or data used incorrectly in the initialisation hase can result in isleading siulation oututs. A coarison between the exeriental and nuerical siulation results conducted by Hill et al. [1] in their investigation into the otion resonse of naval landing craft showed a significant difference in the roll otion frequency. Hill et al. [1] attributed this discreancy to the nuerical siulation software used and ossible liitations in the calculation of added ass. Further investigations into the issues observed by Hill et al. [1] were conducted by DSO and the outcoes are resented in this reort. On investigation it was deterined that the fundaental cause of the discreancy observed by Hill et al. [1] was that they used a roll radius of gyration (roll gyradius) inut in the software siulation that had been deterined exerientally and did not include the effects of hydrodynaic added ass. he software used by Hill et al. [1] requires the roll gyradius to include the effects of added ass. So although the roll gyradius easured by Hill et al. [1] was accurate, it was not aroriate for use as an inut to their siulation, at least not without a odification to include the effects of added ass. A review of the theoretical forulations of roll otion has confired that the discreancy is due to the oission of added ass effects in the siulation inut data. Identifying the direct cause of the discreancy roted a ore considered assessent of the issues exerienced by Hill et al. [1]. It was concluded that the causal factors that led to the incorrect data being used in the siulation were: 1. he secification of the roll gyradius data requireent was abiguous.. No foralised or traceable guidance was available to the exerienter or analyst regarding the secification of the required roll gyradius data and which ethod to use to deterine the aroriate roll gyradius. 3. here was liited or no inforation that described the quality of the ethods available to deterine the roll gyradius.

4 A qualitative and quantitative review of the available ethods of deterining the roll gyradius of a latfor odel, whether hysical or virtual, has been conducted to address these issues and suort the develoent of a set of solutions. he results of the review indicate that the ost aroriate ethod for deterining the roll gyradius of a hysical odel is to conduct an in-water roll decay test using a non-contact otion sensing syste. his ethod roduces a result that includes the effects of added ass. Where a roll decay test cannot be conducted, the roll frae ethod is an effective alternative and has been shown to rovide accurate data. However, additional effort is required to deterine the added ass coonent using stri theory based analysis software. In cases where only a virtual odel of the latfor exists, a couled coutational ethod using couter aided design solid odelling and stri theory based analysis software can be used to deterine the roll gyradius. A function and erforance evaluation of the existing large and sall roll frae devices oerated by the Australian Maritie College and used by DSO has indicated that under aroriate loading conditions the sall roll frae will roduce an accurate easureent of a odel s roll gyradius. However, structural liitations inherent in the roll frae design have been shown to result in frae deforation when under heavy odel loads. he deforation will cause isalignent and robably lead to an adverse level of error in the easureent result. hese issues can be resolved through further analysis and design odification. he results of the investigations resented in this reort have been used to develo a solution to address the issues encountered by Hill et al. [1] and rovide guidance for future exeriental and nuerical investigations. he solution corises: 1. A textual telate for rearing a requireents stateent to define the roll gyradius of a latfor and load condition.. A Decision ree to infor and guide the exerienter and analyst as to the ost aroriate ethod of deterining the roll gyradius of a latfor odel, whether hysical or virtual. 3. hree technology and rocess oriented syste level solutions to deterine the roll gyradius of a latfor. By ileenting the research outcoes and solutions detailed in this reort DSO and the Australian Maritie College will be able to rovide additional assurance of the quality of the research conducted to evaluate aritie latfor shi otions in suort of the Royal Australian Navy and broader Australian Defence Organisation.

5 Author Edward Dawson Maritie Division Edward Dawson is a Research Scientist with the Australian Defence Science and echnology Organisation. He holds a Bachelor of Engineering (Naval Architecture) and a Master of Philosohy (Hydrodynaics) fro the University of asania. Prior to joining DSO Edward worked in the Australian coercial and Defence aritie industry as a consulting engineer. In his current role, Edward is rincially involved in the weaons and cobat systes effectiveness and analysis technology doain.

6 his age is intentionally blank

7 DSO-N-140 Contents ACRONYMS AND ABBREVIAIONS NOMENCLAURE AXIS CONVENION 1. INRODUCION Study Objectives and Outcoes.... HEOREICAL BACKGROUND Roll Period, Roll Gyradius and Added Mass MEHODS O DEERMINE ADDED MASS AND ROLL GYRADIUS Deterining Added Mass in Roll Roll Gyradius: Discrete Eleent Method Roll Gyradius: Couter Aided Design (CAD) Method Roll Gyradius: Physical Measureent Methods Coound Pendulu Roll Frae Roll Decay est Suary SENSIIVIY SUDIES AND UNCERAINY ANALYSES Sensitivity Study Roll Frae: Roll Gyradius Inclining est: Metacentric Height Roll Decay est: Roll Gyradius General Uncertainty Analyses Roll Frae est: Roll Gyradius (in air) Inclining est: Metacentric Height Roll Decay est: Roll Gyradius (in water) Discrete Eleent Method: Discretization Sensitivity Analysis Suary SOLUIONS Procedural Guidance Syste Level Solutions CONCLUDING REMARKS ACKNOWLEDGEMENS... 9

8 DSO-N REFERENCES APPENDIX A: APPENDIX B: APPENDIX C: DECISION REE: MEHOD O DEERMINE A PLAFORM S ROLL GYRADIUS ROLL FRAME FUNCION AND PERFORMANCE EVALUAION B.1. est Setu, Procedure and Results B.. Coarison with CAD Method B.3. Design Issues B.4. Suary GENERAL UNCERAINY ANALYSES: DERIVAION OF ERROR PROPAGAION EQUAIONS C.1. Roll Frae est: Roll Gyradius (in air) C.. Inclining est: Metacentric Height C.3. Roll Decay est: Roll Gyradius (in water)... 51

9 DSO-N-140 Acronys and Abbreviations AMC BNC CAD DAQ DC DSO HP NCMEH OFA PC SHS XCG YCG ZCG Australian Maritie College Bayonet Neill-Concelan Couter Aided Design Data acquisition Direct current Defence Science and echnology Organisation Hewlett Packard National Centre for Maritie Engineering and Hydrodynaics One factor at a tie Personal couter Square hollow section Location of the centre of volue or ass in the longitudinal axis Location of the centre of volue or ass in the transverse axis Location of the centre of volue or ass in the vertical axis Noenclature A Added ass in roll (kg- ) b Daing (kg-) c Stiffness (N-/rad) g Acceleration due to gravity [9.81] (/s ) GM ransverse etacentric height [GM = KM -KG] () h Distance fro coound endulu ivot oint and odel centre of gravity () h F Distance fro coound endulu ivot oint and coound endulu frae centre of gravity () h P Distance fro roll frae endulu ivot oint and roll frae centre of gravity () i Eleent nuber (i th eleent) I Virtual roll oent of inertia (kg- ) I F Moent of inertia of coound endulu [frae only] (kg- ) I Syste Moent of inertia of coound endulu syste [frae and odel] (kg ) I Roll ass oent of inertia (kg- ) k Added ass roll radius of gyration ()

10 DSO-N-140 k Virtual roll radius of gyration () KG KM k M F P n φ d Vertical location of the centre of gravity [above the keel] () ransverse etacentre () Roll radius of gyration () Cobined ass of the latfor and inclining weight (kg) Mass of odel (kg) Mass of coound endulu frae (kg) Mass of odel (kg) Roll frae endulu ass (kg) Natural eriod (sec) Natural roll eriod (sec) Daed roll eriod (sec) V Volue ( 3 ) w x y z Δ Weight of eleent (kg) Princial axis in longitudinal direction (ositive forward) Princial axis in transverse direction (ositive to ort) Princial axis in vertical direction (ositive down) Dislaceent (or ass) of latfor (kg) Δ Virtual dislaceent (or ass) of shi [Δ = Δ + δδ] (kg) δi Added ass coonent of roll ass oent of inertia (kg- ) δδ θ ν π ω n Added ass coonent of dislaceent (or ass) of shi (kg) Angle of incline (deg) Decay constant Pi [3.1416] (constant) Natural frequency (rad/sec) Axis Convention x y z φ Longitudinal direction, stern to bow, ositive forward ransverse direction, ort to starboard, ositive to starboard Vertical direction, baseline to deck, ositive uwards Rotation about x axis, ositive roll to ort

11 DSO-N Introduction Recent research into the dee water roll behaviour of landing craft hull fors using nuerical and exeriental ethods, conducted by Hill et al. [1], has highlighted issues with the alication of existing exeriental rocedures and equient to deterine the roll gyradius of a hysical shi odel. When coleting a coarison between the exerientally easured and nuerically redicted roll decay otion Hill et al. [1] observed a significant hase difference in the roll otion frequency. An exale of the observed hase difference is shown in Figure 1. o enable the validation of nuerical shi otion rediction tools and conduct analyses of latfor otion behaviour, it is ierative that the user inut latfor geoetry and ass roerties are correct. Inaccurate inut data can result in inaccurate and isleading shi otion siulation results. Figure 1 Coarison of exeriental and nuerical roll decay data for a generic landing craft hull for (Adated fro Hill et al. [1]). Investigations by the author have indicated that the discreancy observed by Hill et al. [1] is likely to be attributed to the values of the etacentric height (GM ) or the roll gyradius (k ) or both that were inut as initial conditions in Hill et al. s [1] nuerical siulation. Furtherore, the cause of the difference in the roll gyradius is likely to be due to the absence of added ass in the easureent of the roll gyradius of the exeriental odel. Hill et al. s [1] exerients were conducted at the Australian Maritie College (AMC) in Launceston, asania. he current ethods eloyed by the AMC to deterine the etacentric height and the roll gyradius of a hysical odel are to conduct an in-water inclining test and a free decay oscillation test using a roll frae, resectively. In both 1

12 DSO-N-140 instances these ethods are aroriate for deterining the hysical characteristics of the odel; however, by virtue of the roll frae easureent rocedure and set-u, the easured roll gyradius does not account for the added ass coonent of the odel when oscillating in a viscous liquid. Consequently, the roll frae roll gyradius cannot be used as an initial condition in nuerical siulations where the odelled latfor is floating in a liquid; at least not without due consideration of the latfor s added ass. he effect of the added ass on the roll oent of inertia and consequently roll eriod is shown in Figure 1 where the in air roll gyradius roduces a resonse with a longer eriod of oscillation than that easured for the odel oscillating in fresh water. As discussed by Hill et al. [1], the exeriental ethod adoted in their investigation involved using the roll frae to deterine the roll gyradius of the hysical odels. Nonetheless, the siulation software used by Hill et al. [1] requires an in-water roll gyradius as an initial inut. On further investigation it was concluded that the fundaental issues encountered by Hill et al. [1] were: 1. he secification of the required odel roll gyradius was abiguous. his is likely to be attributed to the lack of inforation suorting the rincial requireent and the intended alication of the test results. he secification of the latfor roll gyradius did not contain secific inforation to qualify the conditions under which the roll gyradius value ertained.. An exlicit stateent of guidance did not exist to direct the exerienter/analyst to the aroriate ethod for deterining the roll gyradius of their latfor with resect to their intended analyses. 3. here was liited inforation describing the quality of the ethods available to deterine the roll gyradius of the latfor. Due to this lack of inforation the exerienter/analyst was not able to ake an infored decision as to which test ethod to use. In resonse to the issues raised in this investigation, a ethod of accurately deterining the ass roerties of hysical odels and full scale latfors oscillating in a liquid is required to enable the easureent or rediction of latfor roll resonse using exeriental ethods or nuerical siulation tools, resectively. 1.1 Study Objectives and Outcoes he rincial objectives of this study are to: 1. Qualify the assertion that the discreancy observed by Hill et al. [1] is due to the use of a roll gyradius that does not include the effects of hydrodynaic added ass.. Investigate the effectiveness and accuracy of the existing ethods to easure or redict the roll gyradius of a hysical or virtual odel. 3. Establish an exeriental aroach to easure the roll gyradius of a hysical odel in cal water.

13 DSO-N Establish a ethod for redicting the roll gyradius, and hence roll eriod, for a hysical odel (and full scale shi) without need for exerient. 5. Quantitatively and qualitatively evaluate the erforance of the existing roll frae device and test ethod used to deterine the roll gyradius of a hysical odel. he results of the roll frae function and erforance evaluation are resented in Aendix B. he outcoes of this research will include, but not be liited to: 1. A quantitative evaluation of the roinent and alicable ethods of deterining the roll gyradius of a hysical or virtual odel.. he roosal of a ethod for deterining the roll gyradius of a latfor without need for exerient. 3. A solution set to overcoe the issues exerienced by Hill et al. [1] and suort the future needs of exerienters and analysts involved in the analysis of aritie latfor otion resonse. 3

14 DSO-N-140. heoretical Background his section resents the theoretical forulation of the roll gyradius of a floating body and the inter-relationshi between roll gyradius, added ass and roll eriod..1 Roll Period, Roll Gyradius and Added Mass It is widely reorted that the natural roll eriod ( φ ) of a shi or floating latfor is a function of its roll gyradius (k ) and transverse etacentric height (GM ), see for exale [-5]. he theoretical relationshi between the un-daed roll eriod, roll gyradius and etacentric height is resented in Equation 1. π k φ = Equation 1 g GM his relationshi is considered to exist where the roll otion is isochronous (of equal interval) and the angle of roll (φ) is no greater than ±10 degrees [5]. It is noted that this forulation does not exlicitly account for the effects of added ass (the virtual ass of the floating body). Due to the effects of added ass the roll gyradius of a floating latfor will be greater than the roll gyradius redicted or easured in air or indeendent of fluid interaction. Considering the effects of added ass, the relationshi between the latfor s roll gyradius and ass can be derived and is resented in Equation. I + A k = Equation It is the roll added ass (A ) coonent that causes the latfor s roll gyradius easured in air to be different to the roll gyradius of the latfor when oscillating in water. he difference between the in air and in water roll gyradius results in a roortional difference in the roll eriod. Rawson and uer [5] reort that the effect of added ass can lead to an increase in roll gyradius of aroxiately 10 to 30 ercent; however, this varies significantly with hull for geoetry and latfor tye. Bhattacharyya [] rovides a ore detailed derivation and exlanation of the effect of added ass. In this instance, the virtual ass oent of inertia of the shi is reresented by I as is shown in Equation 3. Here the added ass coonent is reresented by δδ. I ' = k g δ + k g = ' g k Equation 3 Bhattacharyya [] also reorts that the added ass oent of inertia in roll for a latfor is aroxiately 0 ercent of the dislaceent. Alternatively, the virtual ass oent of inertia relationshi can be reresented in ters of a virtual roll gyradius as shown in Equation 4. 4

15 DSO-N-140 I ' ' '' ( k + k ) = k = Equation 4 g g he virtual roll gyradius (k ) is tyically resented as a ercentage of the latfor s axiu waterline bea (B) and is frequently reorted as being in the region of 0.30B k 0.45B deending on the latfor tye []. Since the virtual roll gyradius is directly related to the added ass of the body, Equation can be reresented as Equation 5. I + A k" = Equation 5 It is the virtual roll gyradius that will rovide the correct roll eriod when coaring the calculated value (Equation 1) with a hysical easureent conducted in water. he theoretical reresentations resented so far do not exlicitly account for the effects of daing on the roll resonse of the latfor. For coleteness, the relationshi between the un-daed and daed roll eriod and gyradius is resented here. As art of the solution to the equation of otion of floating body rolling in cal water, the roll velocity deendent daing ter (b) is reresented by Equation 6. b ν = Equation 6 I' Here b is the roll velocity related daing ter in the equation of otion (Equation 7). d φ dφ I ' + b + GM φ = 0 Equation 7 dt dt he daed frequency of oscillation in roll is related to the un-daed frequency of oscillation as shown in Equation 8. ω = ω φ ν Equation 8 d Consequently, the daed roll eriod becoes: π d = ω Equation 9 ν φ Bhattacharya [] reorts that the effect of daing is to increase the roll eriod, but also that this effect is tyically negligible due to the relative agnitude of the incident roll daing exerienced by tyical shi shaed latfors. It is therefore accetable to consider the daed and un-daed roll eriods to be aroxiately equal. 5

16 DSO-N-140 Based on the theoretical forulations resented here and the influence of added ass on roll eriod discussed by Rawson and uer [5] and Bhattacharyya [] it is evident that the discreancy observed by Hill et al. [1] is ost likely to be attributed to the use of an in air roll gyradius as an inut into an in water nuerical siulation. he alternative source of discreancy is the exeriental error in the easureents of the roll gyradius and etacentric height. While these sources of error are not considered to be significant enough to cause the discreancy observed by Hill et al. [1], an evaluation of the agnitude of the exeriental error was coleted and is resented in 4. 6

17 DSO-N Methods to Deterine Added Mass and Roll Gyradius Several ethods exist to deterine the rincial gyradii of a body and the added ass that is induced by its oscillatory otion in a fluid. he following sections rovide an overview of the ethods that are currently used by exerientalists and analysts. 3.1 Deterining Added Mass in Roll wo coon ethods for deterining the added ass of a body oscillating in a liquid are to ake direct easureents (exerientally) or by a nuerical ethod known as stri theory. Stri theory ethods use either the Frank Close Fit or Lewis For forulations to coute the added ass of a secific hull geoetry. Modern nuerical ethods and couter systes have allowed the stri theory aroach to be alied to ost hull tyes and geoetries to calculate the added ass coonents quickly and effectively. For a detailed descrition of the alication of stri theory see, for exale, [, 3, 6]. he relative low cost and tieliness of the stri theory ethod akes it the referred choice in coarison to conducting an exerient, at least for the ajority of alications. yically, all frequency doain seakeeing software codes will calculate the added ass of the hull geoetry for a range of encounter frequencies. herefore, it is a relatively straight forward rocess to deterine the roll added ass (A ) of a latfor with a known hull geoetry. More advanced rogras such as the SHIPMO000 coonent of the FREDYN [7] tie-doain shi otion analysis rogra can coute the added ass of a latfor in dee and shallow water conditions. Research conducted by Inglis and Price [8] has shown that the added ass of a latfor will differ between dee and shallow water conditions with the general behaviour indicating an increase in added ass with a reduction in water deth. 3. Roll Gyradius: Discrete Eleent Method he discrete eleent ethod used to calculate a latfor s roll gyradius involves taking the first ass oent of each ass eleent on-board the latfor about the global centre of gravity. hat is, the latfor is discretized into eleents of ass and the oent of these eleents are taken about the latfor s centre of gravity in ters of the relative lateral and vertical distance to the eleents individual centre of gravity []. his rocedure is best reresented by Equation 10 where w i is the ass of an individual eleent and y i and z i are the lateral and vertical distances between the eleent s centre of ass and the latfor s global centre of gravity, resectively. ( y + z ) wi i i k = Equation 10 7

18 DSO-N-140 It should be noted that this ethod will rovide the roll radius of gyration indeendent of the environent in which it is oerating and therefore does not account for added ass. his ethod can be used for any size latfor fro odel to full scale. However, its accuracy is constrained by the level of discretization and the easureent uncertainty of the weight and distance of each of the eleents. 3.3 Roll Gyradius: Couter Aided Design (CAD) Method here are currently any couter aided design (CAD) software rogras that include routines (coands) for calculating the area, volue and ass roerties of surface and solid odel objects. he Rhinoceros 3D [9] CAD software rogra is used in this study to investigate its alication and ability to calculate the gyradii of solid object CAD odels reresenting hysical odels. he ethod to deterine the ass roerties of a solid object rograed within the Rhinoceros 3D CAD software involves the use of surface integrals and nuerical integration techniques. In this instance, the Roberg integration ethod is used as it also rovides an estiate of the integration error. he volue of each object is calculated using Stokes theore to reresent the volue as the surface integral of the object s boundary [10]. he volue oent of inertia of a body about its own axis, relative to a global axis, is defined by Equation 11. In this instance it is assued that the body is aligned such that its roll rotational otion is about the x axis. In Equation 11 the first two integrals reresent the second oent of inertia, the second two integrals reresent the first oent of inertia and the final ter reresents the arallel axis transforation. he volue oent of inertia has the units of 5. I = ( y ) X y dv + z dv y0 y dv z0 z dv + V 0 + V V V V z 0 Equation 11 he roll gyradius of the body is sily calculated using the volue oent of inertia about the x axis and the total volue of the body (Equation 1). In this instance, the calculation is indeendent of density. If ultile coonents of varying density are odelled, then either searate calculations would be required for each set of objects with a coon density or a ass secific routine should be used. I k = X Equation 1 V 3.4 Roll Gyradius: Physical Measureent Methods Coon ethods to hysically easure roll gyradius are to use either a coound endulu or a roll frae. hese devices are very ractical for deterining the roll oent of inertia of scale odels. An alternate ethod is to conduct an unconstrained roll decay test with the odel floating in water. he difference between the 8

19 DSO-N-140 endulu/frae and roll decay test is that the later ethod accounts for the effects of hydrodynaic added ass Coound Pendulu In the case of the coound endulu the shi odel is held in a stiff but light frae which is susended centrally below a ivot oint as shown in Figure. he distance fro the odel s vertical centre of gravity and the ivot oint is denoted by h. he ass, centre of gravity and oent of inertia of the frae ust also be deterined. he frae s oent of inertia is deterined by conducting the free oscillating test with the frae only. Figure Coound Pendulu with shi odel (End View) [4]. hen the frae and the odel are dislaced by a sall angle about the ivot oint and released. As the frae and frae with odel configurations oscillate freely fro side to side the natural eriod of oscillation is easured by recording the tie for the frae to colete a set nuber of oscillations [4]. Lloyd [4] suggests ten oscillations; however, if a recise and accurate tie easureent syste is used the nuber of oscillations ay be reduced. he initial angle to which the frae is rotated ay have an effect on the accuracy of the easureent. As with any easureents it would be rudent to reeat the rocess several ties. he roll radius of gyration is deterined by the following relationshi as resented by Lloyd [4]. Using the arallel axis theore, the cobined oent of inertia of the frae and odel syste is: I = k + h + I Equation 13 Syste F he stiffness of the coound endulu is: ( h ) c = g + h F F Equation 14 he natural frequency of oscillation of the syste is: 9

20 DSO-N-140 ω n = π = n I c Syste Equation 15 Finally, the radius of gyration of the odel is given by: k = g ( h + h ) F 4π F n h I F Equation Roll Frae An alternate device to the coound endulu is the roll frae. his device, shown in Figure 3, is currently used by the National Centre for Maritie Engineering and Hydrodynaics (NCMEH) at the Australian Maritie College in Launceston, asania. Figure 3 AMC Roll Frae with hysical shi odel [11]. he roll frae uses a siilar aroach to the coound endulu syste resented by Lloyd [4] where the odel is held in a suort frae and is rotated about a ivot oint. he eriod of oscillation of the frae and the frae and odel cobined are easured by rotating the frae to an initial angle and releasing the. he ass of the odel and the righting weight are also easured. he radius of gyration is calculated using the relationshi resented in Equation 17. k ( ) g h 1 = Equation

21 DSO-N-140 his relationshi can be derived fro the ethod roosed by Lloyd [4] for the coound endulu syste as follows. Using the arallel axis theore, the cobined oent of inertia of the frae and odel syste is reresented by Equation 13 and the stiffness of the syste is reresented by Equation 14. he radius of gyration of the syste is reresented by Equation 15. Given the frequency of oscillation of the syste is: ω n = π = n I c Syste Equation 18 he syste s oent of inertia is given by: I Syste c = Equation 19 ω n By substituting Equation 14 and Equation 15 into Equation 19 the oent of inertia becoes: I Syste ( h + h ) F F g n = Equation 0 4π By substituting Equation 0 into Equation 14 the radius of gyration becoes: k = ( h + h ) F F 4π g n h I F Equation 1 he centre of rotation of the odel and frae syste is coincident with its centre of ass. Consequently the height ter (h) becoes zero and the endulu ass and distance ters can be substituted for the frae ass and distance ters resectively. herefore, Equation 1 becoes: k ( h ) P P = g 4π n I F Equation Using Equation for the roll frae and the roll frae and odel systes indeendently, we can deterine the roll radius of gyration for both systes. By subtracting the solution for the roll frae fro the roll frae and odel solution, we can deterine the roll radius of gyration for the odel as shown in Equation Roll Decay est An alternate ethod to deterine the roll gyradius of the odel in air is to easure it in water using a cal water roll decay test. he roll gyradius can be directly calculated fro the etacentric height and the roll eriod of the odel as deterined fro the roll decay 11

22 DSO-N-140 test. he etacentric height can be easured by conducting an in-water inclining test rior to the roll decay test. he roll gyradius can be calculated by transosing Equation 1 to becoe Equation 3 where the average roll eriod ( ) of the odel can be substituted for roll eriod ( φ ). φ Ave k '' φ Ave g GM = Equation 3 π φ he average roll eriod ( Ave ) of the odel is directly easured fro the roll decay trace by identifying the elased tie for a colete oscillation (eak to eak) as shown in Figure 4. he average eriod is calculated using the series of easured eriods (Equation 4). 1 φ Equation 4 i = n Ave = i n i= n Zeroed Data Peak Roll Angle [deg] ie [sec] Figure 4 Exale roll decay test data: tie series roll resonse indicating the eak to eak easureent of the roll eriod. he roll decay otion of the odel can be easured exerientally using a range of sensors and set-u configurations. he AMC currently uses the QUALISYS threediensional digital video otion cature syste installed in its Model est Basin. he syste uses 8 Oqus300 infrared caeras, 16 eranent reference arkers and a iniu of 3 odel borne arker balls to track the three rotational and three translational otions of the odel. he AMC QUALISYS syste ossesses a linear dislaceent easureent accuracy of ± 0.5 illietres and an angular dislaceent easureent accuracy of ± 1

23 DSO-N degrees over a linear arker searation distance of 1000 illietres. he advantage of using a non-contact test syste like QUALYSIS is that it does not introduce external sources of daing into the odel s dynaic syste. 3.5 Suary he roinent and alicable ethods to deterine the added ass and roll gyradius of hysical or virtual latfor odels have been identified and discussed. Each of the ethods described has advantages and disadvantages in the context of alicability (to latfor tye and oerating condition), oerability (ease of oeration), resource requireents (oerating costs and schedule) and accuracy of results. As reviously entioned, the accuracy and the alicability of roll gyradius test results have a significant influence on nuerical shi otion siulation and analysis. Consequently, further analysis and discussion of the accuracy of the ethods used to deterine roll gyradius are resented in the following sections. 13

24 DSO-N Sensitivity Studies and Uncertainty Analyses his section resents the results of the sensitivity and uncertainty analyses coleted to investigate and identify the critical araeters of the hysical test ethods used by DSO and the AMC and rovide a quantitative indication of the uncertainty in each easureent ethod. he ethods analysed are: 1. Deterining roll gyradius using the roll frae. Deterining etacentric height using an inclining exerient 3. Measuring the roll eriod and subsequently deterining the roll gyradius using a free roll decay test. 4.1 Sensitivity Study A local sensitivity analysis of the ethods to easure the etacentric height and roll gyradius was coleted to investigate the effect of error in each easured inut araeter on the error in the outut araeter. his was done using the OFA (one factor at a tie) aroach. In each instance, the OFA ethod is coleted by varying one inut araeter while holding the reaining inut araeters fixed and observing the effect on the outut araeter. In each of the three cases investigated the inut araeters were varied across a range fro -5% to +5%. he initial inut araeter values used as the noinal (baseline) condition were sourced fro a set of exerients conducted by DSO in 011. he test data relates to a generic landing craft hull for (odel AMC shown in Figure 5) that was ballasted in a heavy load condition. he target dislaceent and hydrostatic araeters for the odel in the heavy condition were: k KG GM = kg = 0.15 (in air) = = (KM = at this load condition) Figure 5 Generic landing craft odel AMC

25 DSO-N Roll Frae: Roll Gyradius he forulation of roll gyradius with resect to the roll frae test araeters is reresented by Equation 17. It is reeated below for convenience. g h 4 k = ( ) he following initial inut araeters were recorded during the test conducted by DSO at the AMC in 011: =.584 kg h = =.10 sec =.595 sec = kg he result of the roll frae roll gyradius sensitivity study shown in Figure 6 indicates that the easureent error in the oscillation ties ( 1 and ) are the ost significant contributor to the error in the easureent of k. In addition to this, as 1 and tend towards each other ( 1 ), the change in outut araeter increases significantly for the sae range of change in inut araeter. As 1 and tend away fro each other ( 1 << ) the change in outut araeter reduces and tends towards the change in outut araeter for the cobined change in 1 and, where the change in inut and outut is directly roortional. Change in Outut Paraeter (k ) [%] Figure 6 0% 15% 10% 5% 0% -5% -10% -15% -0% h 1 1 & -7.5% -5.0% -.5% 0.0%.5% 5.0% 7.5% Change in Inut Paraeter [%] OFA sensitivity study results for the roll frae ethod of deterining the latfor s roll gyradius. 1 15

26 DSO-N-140 It can be concluded that, of the easured inut araeters, it is iortant to iniise the easureent error in the oscillation ties, but also to ensure that the eriod of oscillation of the frae and odel ( ) is significantly greater than the frae alone ( 1). his behaviour is also aarent in the asyetric and non-linear resonse of the 1 and curves. Considering the baseline inut values used in this analysis, and neglecting the actual oscillation eriod easureent errors, it would aear that the eriods of oscillation are unfavourably close in agnitude as Figure 6 shows that the change in outut is large coared to the change in inut. he obvious eans to increase the difference between the natural eriods of oscillation of the frae and frae with odel configurations are to increase the eriod of the frae with odel ( ) and/or reduce the frae only eriod ( 1). On insection of the existing roll frae device it is aarent that there is liited scoe to reduce the natural eriod of oscillation of the frae alone. he only changes that can be ileented, without actual hysical odification, are to reduce the endulu ass ( ) and the endulu length (h ). However, any change in these araeters will be observed, albeit to a lesser extent, in the frae with odel condition as the two are not utually exclusive. herefore it is ore effective to increase the natural eriod of oscillation of the frae with odel configuration. his can be achieved by increasing either the ass of the odel ( ) or the roll gyradius (k ) or both. Realising a change like this is not readily ossible as the ass and roll gyradius of the odel are rescribed (fixed) araeters. he only identified alternative to resolve this issue is to atch a odel and roll frae that will result in significantly different eriods of oscillation for the two test conditions. Given the variability in the range of odel size, ass and roll gyradius that are likely to be tested, this becoes a colex engineering design roble. Addressing this articular roble is outside of the scoe of this investigation Inclining est: Metacentric Height he ethod to deterine the etacentric height fro an inclining test is described by Equation 5. As discussed by Lewis [1], the inclining test ethod is aroriate for axiu angles of incline (θ) of ± degrees. d GM = Equation 5 M tanθ he following initial inut araeters were recorded during the test conducted by DSO at the AMC in 011: = 0.60 kg d = = kg M = ( +) = kg θ = 1.11 deg he result of the inclining exerient GM sensitivity study shown in Figure 7 indicates that the influence of the easureent error in each of the inut araeters is aroxiately equal, albeit with no consideration of the direction of their roortionality. he sensitivity of the outut araeter is indeendent of any change in the order of 16

27 DSO-N-140 agnitude of its inut araeters. hat is, for exale, when the inclining ass () was changed fro 0.60 kg to.600 kg or kg there was no change in the relationshi between ercentage change in inut and outut araeter. his behaviour was observed for each of the inut araeters. d θ Change in Outut Paraeter (GM ) [%] 10.0% 7.5% 5.0%.5% 0.0% -.5% -5.0% -7.5% -10.0% -7.5% -5.0% -.5% 0.0%.5% 5.0% 7.5% Change in Inut Paraeter [%] Figure 7 OFA sensitivity study results for the inclining test ethod of deterining the latfor s etacentric height Roll Decay est: Roll Gyradius he forulation of roll gyradius with resect to the roll frae test araeters is reresented by Equation 3. It is reeated below for convenience. g GM k" = φ Ave π he following initial inut araeters were recorded during the test conducted by DSO at the AMC in 011: φ Ave = sec GM = 0.04 he result of the roll decay roll gyradius (k ) sensitivity study shown in Figure 8 indicates that the influence of the easureent error in the roll eriod ( φ Ave ) is the doinant source of uncertainty in the outut araeter. In coarison, the etacentric height has only half the influence of the roll eriod. Considering that atching an exerientally easured and nuerically redicted roll resonse is of significant value to shi otion analyses, it is aarent that it is ore iortant to iniise the error in the 17

28 DSO-N-140 roll eriod inut araeter. he sensitivity of the outut araeter is indeendent of any change in the order of agnitude of the inut araeters. φave GM Change in Outut Paraeter (k" ) [%] 10.0% 7.5% 5.0%.5% 0.0% -.5% -5.0% -7.5% -10.0% -7.5% -5.0% -.5% 0.0%.5% 5.0% 7.5% Figure 8 OFA sensitivity study results for the ethod of deterining the latfor s roll gyradius using a roll decay test. 4. General Uncertainty Analyses A general uncertainty analysis was coleted to investigate the roortion of the uncertainty in each of the easureent ethods for the sae odel and load condition used in the sensitivity study. In each instance the data reduction equation has been analysed using an error roagation aroach to evaluate the uncertainty in the exeriental result. he general uncertainty analysis ethodology used in this analysis follows the ethod resented by Colean and Steele [13]. All uncertainty estiates are quoted at a 95% confidence level. he detailed derivation of the error roagation artial differential equations are resented in Annex C Roll Frae est: Roll Gyradius (in air) Change in Inut Paraeter [%] he data reduction equation used to deterine the roll gyradius is defined by Equation 17. he resulting error roagation equation used to deterine the uncertainty in the roll gyradius (k ) is: 18

29 DSO-N-140 U k k U = ( 1 ) U ( ) U h + h + ( 1 ) U ( ) Equation 6 U + 1 he following uncertainty estiates were recorded during the test conducted by DSO at the AMC in 011: U U h U 1 U U = kg = 0.00 = sec = sec = kg For AMC (011): h 1 =.584 kg = =.10 sec =.595 sec = kg Using the uncertainty estiates that were deterined based on the easureent equient used in the test and the easured test araeters for the odel (AMC-97-07), the calculated roll gyradius and its easureent uncertainty is calculated as follows: U k k (.584) ( 0.584) ( (.595).10 ) 0.05 = ( ) ( ) (.595 (.10) ) ( ) Equation 7 U k = 0.09 =.90% Equation 8 k k = 0.1 ± Equation Inclining est: Metacentric Height he data reduction equation used to deterine the etacentric height (GM ) is defined by Equation 5. he resulting error roagation equation used to deterine the uncertainty in the etacentric height (GM ) is: 19

30 DSO-N-140 U tan GM U U d U + M θ Uθ = + + Equation 30 GM d M ( 1 tan ) + θ he following uncertainty estiates were recorded during the test conducted by DSO at the AMC in 011: U = kg U d = 0.00 U M = kg U θ = deg = 1.745E-3 rad For AMC Run 85 (011): = 0.60 kg d = M = kg θ = 1.11 deg = 1.940E- rad Using the uncertainty estiates that were deterined based on the easureent equient used in the test and the easured test araeters for the odel (AMC-97-07), the calculated etacentric height and its easureent uncertainty is calculated as follows: U GM GM tan = 0.60 ( E ) tan ( 1.940E ) ( ) E Equation 31 U GM = = 1.1% Equation 3 GM GM = 0.04 ± Equation Roll Decay est: Roll Gyradius (in water) he data reduction equation used to deterine the roll gyradius in water (k ) is defined by Equation 3. he resulting error roagation equation used to deterine the uncertainty in the roll gyradius (k ) is: U k '' k '' U = φ φ U GM + GM Equation 34 0

31 DSO-N-140 he following uncertainty estiates were recorded during the test conducted by DSO at the AMC in 011: U φ = 0.00 sec U GM/GM = 1.1% For AMC Run 86 (011): φ Ave = sec GM = 0.04 Using the uncertainty estiates that were deterined based on the easureent equient used in the test, the uncertainty estiate of the etacentric height deterined fro the inclining exerient and the easured test araeters for the odel (AMC-97-07) the calculated roll gyradius (in water) and its easureent uncertainty is calculated as follows: ( 0.00) U '' k = + ( ) '' Equation 35 k U '' k = = 1.81% Equation 36 '' k '' k = ± Equation Discrete Eleent Method: Discretization Sensitivity Analysis A sensitivity analysis was coleted to investigate the effect of object discretization on the gyradius calculated using the discrete eleent ethod. A square anel with an edge length of one etre and a thickness of ten illietres was used as the test object. he anel was discretized into equal sized eleents by dividing its erieter edges by a factor of, 4, 8 and 16 to for four different test sales (Figure 9). Figure 9 Discretized 1 x 1 x 0.01 square anel: (a) n = 4 eleents (b) n = 16 eleents (c) n = 64 eleents (d) n = 56 eleents. he discrete eleent ethod (Equation 10) was used to calculate the anel s radius of gyration about its x-x axis using the four different discretized geoetries. he calculated 1

32 DSO-N-140 result was coared against the analytical solution resented in Equation 38 where a is the edge length of the anel. k 1 = a 1 Equation 38 he results of the coarison indicate that the relative error between the calculated result and the analytical result decreases with a ower function as the level of discretaization is increased (Figure 10). For the unifor square geoetry it was calculated that a iniu of 50 eleents are required to achieve a relative error of one ercent. Based on this result, it is aarent that the alication of the ethod to a highly detailed and colex shi geoetry is rohibitive in the context of accuracy and efficiency. On reflection, the CAD ethod described in 3.3 reresents an efficient ebodient of the discrete eleent ethod and a ore effective alternative to deterining the roll gyradius of a virtual shi geoetry. Eleent Method Analytical Solution Relative Error % k [] % 5% Relative Error 0.0 0% Nuber of Equal Sized Eleents Figure 10 Discretization sensitivity analysis of the eleent ethod: Eleent ethod coared to analytical solution of the gyradius of a 1 x 1 x 0.01 anel. 4.4 Suary he results of the sensitivity and uncertainty analyses indicate the following: 1. When using a roll frae device to deterine the roll gyradius of a hysical odel it is iortant to iniise the error in the easureent of the tie of oscillation as this has the greatest influence on the error of the calculated result.. It is iortant to use a roll frae which has a eriod of oscillation that is significantly less than that of the odel and roll frae cobined. If the eriod of oscillation of the

33 DSO-N-140 frae only and odel with frae configurations are too siilar the influence of an error in the tie easureent on the calculated result increases significantly. 3. For the landing craft odel and load condition used in the receding analyses to deterine its roll gyradius, it is aarent that there is a lower uncertainty in the calculated result using the roll decay test ethod when coared to the roll frae ethod. 4. For the landing craft odel and load condition used in these analyses to deterine the etacentric height using an inclining exerient, the uncertainty in the easureent is low (1.1%) and this easureent ethod is considered to be accetable if conducted in accordance with the rinciles resented by Lewis [14] and using the AMC QUALYSIS syste and oerating rocedures. 5. Based on the sile geoetry analysed to evaluate the erforance of the eleent ethod and the results of the analysis, this ethod has been found to be an inefficient and ineffective way of deterining the roll gyradius of the colex geoetries tyical of aritie latfors. 3

34 DSO-N Solutions In addressing the fundaental issues exerienced by Hill et al. [1], two fors of solution have been identified: the requireent to change existing rograatic (lanning, test and analysis) rocedures and rocesses; and the synthesis of existing test ethods to for functional, syste level solutions. ogether these two fors of solution reresent the holistic solution to the issues encountered by Hill et al. [1] and a qualified and traceable ethod to be used in future test rogras. 5.1 Procedural Guidance wo fors of rocedural guidance have been develoed in conjunction with the syste level solutions resented in 5. to address the issues identified at the start of this investigation. he two issues addressed by the rocedural guidance are: 1. he abiguities in the secification of the required test roll gyradius.. he lack of an exlicit stateent of guidance to direct the exerienter/analyst to the aroriate ethod for deterining the roll gyradius of their latfor with resect to their intended analyses. In addressing the first issue it is roosed that the secification of the roll gyradius requireent for a aritie latfor, whether odel scale of full scale, should be structured using the following forats. When assigning a roll gyradius to a odel or full scale latfor, whether hysical or virtual, the following stateent should be tailored and used: he roll gyradius of the [latfor identifier] in the [load condition descritor] load condition shall be equal to [quantitative value of the roll gyradius] etres ±[required accuracy] etres. he roll gyradius is that of the [latfor identifier] when easured in a [descritor of the ediu in which the roll gyradius is easured: in-water or out of water] condition and therefore [includes/does not include] the effects of hydrodynaic added ass. In instances where an in-water roll gyradius is required, the assigned roll gyradius corresonds to that of the latfor floating in a dee water condition. When reorting on the easureent, coutation or calculation of a latfor s roll gyradius the following stateent should be tailored and included in the reort or data docuent: he roll gyradius of [latfor identifier] in the [load condition descritor] load condition has been deterined to be [quantitative value of the roll gyradius] etres ±[include uncertainty estiate] etres. he roll gyradius was deterined using the [easureent ethod descritor] ethod and reresents the latfor when in a [dry, out of water/ in water] condition. 4

35 DSO-N-140 In addressing the second issue, a rocess flowchart (Decision ree) has been develoed to rovide guidance to the analyst/exerienter as to which of the roosed syste level solutions, resented in 5., should be eloyed to deterine the roll gyradius of a latfor. he latfor ay be either a hysical scale odel (coonly used for scale odel exerients in a hydrodynaic test facility) or a virtual odel. he virtual odel ay be of a concetual latfor design, a couter rototye of a hysical scale odel (used for the urose of exerient design), or an existing full scale latfor. he Decision ree is resented in Aendix A. he activities catured in the Decision ree assue that the exerienter/analyst is caable of conducting each activity or at least has access to resources that can rovide the data outut fro the activities. Following the Decision ree does not assure the quality of the outcoes of each activity nor the data used as inuts to the activities. 5. Syste Level Solutions hree syste level solutions have been identified based on the theoretical forulation of roll gyradius and added ass resented in, the available ethods of deterining these two araeters discussed in 3 and the quantitative evaluation of the erforance of these ethods resented in 4. he solutions address the following investigation objectives resented in 1: 1. Establish an exeriental aroach to easure the roll gyradius of a hysical odel in cal water.. Establish a ethod for redicting the roll gyradius, and hence roll eriod, for a hysical odel (and full scale shi) without need for exerient. he syste level solutions are: 1. Conduct an in-water inclining test and roll decay test for the odel in its ballast condition.. Conduct an in-air oscillation test using a roll frae device to deterine the odel's in-air roll gyradius. he roll frae has been chosen in reference to the endulu ethod due to its ortability and ease of oeration. A correction for the in-water roll gyradius is required and can be achieved by using a nuerical aroach to calculate the roll added ass coonent at the natural roll frequency. 3. Couter odelling: Use of a CAD solid odelling rogra to odel the hysical geoetry and calculate its rincial gyradii (including the roll gyradius). A correction for the in-water roll gyradius is required and can be achieved by using a nuerical aroach to calculate the roll added ass coonent at the natural roll frequency. Where a detailed CAD solid odel is not available, or the effort to generate one is too great, this data ay be relaced by the latfor s ass distribution data or a roll gyradius deterined eirically and based on the latfor tye and load condition. 5

36 DSO-N-140 he identified resource requireents, advantages and disadvantages of each of these solution otions have been collated and are resented in able 1. When selecting one of the roosed solutions, the analyst should give consideration to the oerational requireents and constraints that are unique to its alication. 6

37 able 1 Resource requireents, advantages and disadvantages of roll gyradius easureent and rediction ethods. Method Resource Requireents Advantages Disadvantages 1. In-Water Roll Decay est. Roll Frae Measureent and Added Mass Calculation 3. CAD Modelling Calculation & Added Mass Calculation Physical odel Model in ballasted condition Model hydrostatic data est facility Motion easureent, data acquisition and ost-rocessing syste Physical odel Model in ballasted condition Roll frae device Motion easureent, data acquisition and ost-rocessing syste Hull geoetry in CAD forat (surface odel) Added ass calculation caable software Hull geoetry in CAD forat (surface and solid odel) Load condition data Added ass calculation caable software Suleentary data: detailed ass distribution reorted or easured roll eriod and associated load condition when eriod was recorded Directly alicable to scale odels. his ethod allows the exerienter to assign the required odel ballast condition (KG and k ) and conduct seakeeing tests iediately. No CAD latfor odelling or added ass coutations are required. he easureent can be conducted indeendent of a test facility (test basin or towing tank facility tie is not required). he odel is directly and easily accessible. his enables tiely and accurate odification to the ballast condition. Suitable for furnishing the siulation requireents of any latfor of any scale. No hysical odel or easureent activity is required. Modifications to odel geoetry and load condition can be coleted quickly. Various load conditions can be calculated and analysed with inial effort. his ethod can be used for rototying and/or designing exeriental odels. DSO-N-140 he test requires the use of a facility of adequate size to accoodate the odel and rovide clearance to itigate interference fro reflected waves fro all rigid boundaries (tank walls). his ethod rovides an outut that is targeted at conducting subsequent odel tests. Additional inforation and effort is required to deterine the added ass coonent that will act on the latfor. A CAD and added ass or shi otion rediction rogra are required. he analyst ust odel the hysical latfor in each load condition in order to redict the corresonding added ass coonent. Detailed ass distribution data is required for the lightshi condition to deterine the actual roll gyradius of the latfor. However, a reresentative roll gyradius value can be used in way of this calculation. Soe additional work is required to deterine the added ass coonent that will act on the latfor. 7

38 DSO-N Concluding Rearks When conducting nuerical shi otion siulation and analysis it is iortant to ensure that the siulation inut data is accurate and correct. Incorrect data or data used incorrectly will result in erroneous and isleading siulation results. he disarity in roll frequency observed by Hill et al. [1] in their exeriental and nuerical analysis of landing craft roll otion has led to further investigation to identify the causes of their results. Based on the outcoes of the current investigation it can be concluded that the root cause of the issue exerienced by Hill et al. [1] was the incorrect alication of their easured roll gyradius data. he discreancy observed in their results is redoinantly due to the absence of the influence of added ass. Nonetheless, this issue roted further investigation into the rocess, rocedures and equient used to deterine the araeters that influence the roll otion of a latfor: the roll radius of gyration and the transverse etacentric height. he solution to the issues identified throughout this investigation corise: the introduction/establishent of a requireents stateent aroach to unabiguously defining the data need; the forulation of a Decision ree tye guidance tool for the exerienter/analyst; and three technology/rocess based syste level ethods for deterining the roll gyradius of a latfor. Furtherore, the results of these investigations have shown that of the roinent ethods to hysically easure the roll gyradius of a scale odel, the in-water roll decay test is the ost effective and accurate. he in-water roll decay test ethod rovides a roll gyradius value that includes the effects of hydrodynaic ass, ossess low easureent uncertainty and results in the odel being ballasted and reared for the actual hydrodynaics test rogra. Notwithstanding this outcoe, the roll frae device is also caable of roviding an accurate roll gyradius easureent, albeit without the effects of added ass. he roll frae ethod is a suitable alternative to conducting an in-water test which requires ore resources to be allocated. An evaluation of the function and erforance of the existing AMC roll fraes has indicated that there are liitations associated with the structural integrity of the dynaic frae that ay result in increased easureent error under secific testing conditions. his issue is ore ertinent to the large roll frae currently oerated by the AMC. Further analysis and design odification is required to resolve the issues associated with the current roll fraes; however, this is outside of the scoe of this investigation. he ethod of conducting an in-water inclining exerient to deterine a odel s transverse etacentric height and location of its vertical centre of gravity has also been found to roduce an accurate result with accetable easureent uncertainty. he ost effective alternative to hysically easuring the roll gyradius of a latfor is to use a couled coutational aroach. In this case, the in-air roll gyradius of a latfor of any size can be deterined using three-diensional solid odelling CAD software. he in-water roll gyradius can then be deterined by couting the hydrodynaic added ass using a stri theory based software rogra. 8

39 DSO-N Acknowledgeents he author wishes to thank the following eole for their assistance while conducting this investigation: Ms eresa Magoga for her assistance in using Maestro to conduct the structural analysis of the roll fraes; Mrs Jenny Hill for her assistance when conducting the roll frae tests; and Mr Shaun Denehey and Mr Kirk Meyer of the AMC for their assistance in setting u the roll frae and the data acquisition syste. 9

40 DSO-N References 1. Hill, J., et al., Investigation into the Roll Behaviour of Landing Craft in Dee Water, in PACIFIC 01 International Maritie Conference. 01: Sydney, Australia Bhattacharyya, R., Dynaics of Marine Vehicles. 1978, New York, USA: Wiley. 3. Lewis, E.V., Princiles of Naval Architecture: Motions in Waves and Controllability. Vol , Jersey City, USA: Society of Naval Architects and Marine Engineers. 4. Lloyd, A.R.J.M., Seakeeing: Shi Behaviour in Rough Waves. 1989, Sussex, England: Ellis Horwood. 5. Rawson, K.J. and E.C. uer, Basic Shi heory. 001, Oxford, England: Butterworth Heineann. 6. Frank, W. and N. Salvensen, he Frank Close-Fit Shi-Motion Couter Progra. 1970, Naval Shi Research and Develoent Center: Washington D.C. 7. MARIN, FREDYN Version 10.3 Couter Progra for the Siulation of a Steered Shi in Extree Seas and Wind. 011, CRNAV, Maritie Research Institute Netherlands. 8. Inglis, R.B. and W.G. Price, Motions of Shis in Shallow Water. ransactions RINA, : Robert McNeel and Associates, Rhinoceros NURBS Modelling for Windows. 011: Seattle, Washington. 10. Arden, G., Descrition of Method for Calculating Mass Proerties of Solids E. Dawson, Editor. 013, Robert McNeel & Associates: Melbourne Macfarlane, G.J., Develoent of Shi Dynaics Deonstration Models, in Coittee for University eaching and Staff Develoent. 1998: Launceston, asania. 1. Lewis, E., ed. Princiles of Naval Architecture: Stability and Strength. Vol. I. 1988, Society of Naval Architects and Marine Engineers: New Jersey, USA. 13. Colean, H.W. and W.G. Steele, Exerientation and Uncertainty Analysis for Engineers. 1999, United States of Aerica: John Wiley & Sons. 14. Lewis, E.V., ed. Princiles of Naval Architecture: Stability and Strength. Vol , Society of Naval Architects and Marine Engineers: Jersey City, USA. 15. Macfarlane, G., Roll Frae Error Sources, J. Hill, E. Dawson, and. urner, Editors. 011, Australian Maritie College: Launceston, asania. 16. Advanced Marine echnology Centre, MAESRO , DRS Defence Solutions: Stevensville, USA. 17. International owing ank Conference. Recoended Procedures. 008 Seteber 011]; Available fro: htt://ittc.snae.org/docuents.ht. 18. Miller, M.P., An Accurate Method of Measuring the Moents of Inertia of Airlanes. 1930, National Advisory Coittee for Aeronautics: Washington D.C. 30

41 Aendix A: Decision ree: Method to Deterine a Platfor s Roll Gyradius DSO-N-140 he roll gyradius of a latfor odel is required Is the latfor odel a scale hysical odel or a virtual odel (scale or full size)? Virtual Scale Physical A B Figure A1 Decision ree: Start of roll gyradius deterination rocess. 31

42 DSO-N-140 A High fidelity solid CAD odel of latfor Detailed latfor ass distribution data Calculate the roll gyradius (in air) fro CAD odel and/or weight data Platfor load condition data for required test condition/configuration CAD odel of latfor hull geoetry OR hull offset data Yes, include Calculate added ass of latfor hull using software (stri theory or otential flow) ethod Is the requireent for the roll gyradius to include added ass? No, exclude Roll gyradius of virtual latfor odel (excluding added ass) deterined Roll gyradius of virtual latfor odel (including added ass) deterined Figure A Decision ree: virtual odel decision solution route (virtual odel includes a nuerical odel of a latfor that can be either existing or concetual and of any scale). 3

43 DSO-N-140 B High fidelity solid CAD odel of latfor CAD odel of latfor hull geoetry OR hull offset data Platfor load condition data for required test condition/configuration Yes, include Is the requireent for the roll gyradius to include added ass? No, exclude Detailed latfor ass distribution data No Can the test be conducted in-water (in a tank)? Yes Yes Can the test be conducted in-water (in a tank)? No Calculate added ass of latfor hull using software (stri theory or otential flow) ethod Conduct roll frae test to deterine roll gyradius (k ) Conduct in-water inclining test to deterine GM Conduct in-water inclining test to deterine GM Calculate the location of the vertical centre of gravity fro CAD odel Conduct in-water roll decay test to deterine roll gyradius Conduct roll frae test to deterine odel s roll gyradius Conduct roll frae test to deterine odel s roll gyradius Roll gyradius of virtual latfor odel (including added ass) deterined (k ) Roll gyradius of virtual latfor odel (including added ass) deterined (k ) Roll gyradius of latfor odel (excluding added ass) deterined (k ) Roll gyradius of latfor odel (excluding added ass) deterined (k ) Figure A3 Decision ree: scale hysical odel decision solution route. 33

44 DSO-N-140 Aendix B: Roll Frae Function and Perforance Evaluation he function and erforance of the sall AMC roll frae (Figure B1) were investigated and evaluated by conducting a series of tests to deterine the roll radius of gyration of a sile ontoon odel (AMC-03-10) and coaring the results to the roll gyradius deterined using the CAD ethod. he objectives of the function and erforance evaluation tests were to: 1. Investigate the effects of initial roll angle on the roll gyradius test result.. Investigate the effects of the oscillation tie easureent syste on the roll gyradius test result. 3. Evaluate the user oeration rocedure and the syste function to identify any liitations. 34

45 DSO-N-140 Z Y X Figure B1 AMC Roll Frae (sall). Annotations: 1. Lateral locating oints for dynaic frae longitudinal suorts (tyical);. Bearing and shaft arrangeent (non-endulu end); 3. Roll axis; 4. Dynaic frae (assebly); 5. Longitudinal locating oints for underslung suorts (tyical); 6. Locating hole for lateral securing rods (rods not shown) (tyical); 7. Under-slung suorts (sub-assebly); 8. Bearing and shaft arrangeent (endulu end); 9. Pendulu weight locating and locking nuts (uer endulu); 10. Static frae (assebly); 11. Pendulu to dynaic frae interface (sub-assebly); 1. Pendulu ar (threaded rod); 13. Pendulu weight locating and locking nuts (lower endulu); 14. Pendulu weight. he sall AMC roll frae can be used to deterine the roll radius of gyration of odels with an overall length of u to 1.65 etres and an overall bea of u to 0.75 etres. here are; however, liitations related to the axiu erissible ass of the odel due to the structural integrity of the roll frae. hese issues are discussed in B.3. B.1. est Setu, Procedure and Results he evaluation tests were coleted using a sile ontoon odel. he odel was selected because of its regular and flat sided shae which resulted in a relatively easy setu and easureent rocess in the roll frae device. Its regular shae and accessible 35

46 DSO-N-140 internal arrangeent also ade it easy to survey and odel the ontoon using the Rhinoceros 3D CAD rogra. A rendered iage of the three diensional CAD solid odel of the ontoon is resented in Figure B. Z Y X Figure B Pontoon odel AMC-03-10: overall length = 1.340, overall bea = 0.363, overall height = 0.50, ass in air = kg. he location of the vertical centre of gravity of the odel was deterined by assuing a hoogenous aterial density and using Rhinoceros 3D to calculate the centre of volue of the three diensional odel. his enabled the odel to be aligned to the roll axis of the roll frae during the roll frae test. wo tie easureent ethods were used. hese were the: 1. wo erson anual ethod with each erson uses a digital stowatch (this reresents the existing AMC test rocedure).. Integrated laser encoder and digital data acquisition syste. he integrated laser encoder syste architecture is resented in Figure B3. he laser encoder syste was configured to record a voltage signal fro the encoder at a saling frequency of 1000 Hz using a PC based National Instruents LabView data acquisition syste. A sall wooden stave was adhered to the dynaic frae to act as the bea breaker and trigger a sike in the voltage signal (Figure B4). An exale of the recorded signal is shown in Figure B5 where each successive ulse in the free oscillation hase reresents the stave crossing the laser bea. he tie between each ulse equates to half of the natural roll eriod. It can be observed that as the roll otion decays and the roll alitude and velocity decrease, the signal ulses develo a flat region at their local inia. his reresents the tie taken for the width of the stave to ass in front of the laser bea. he eriod of oscillation was deterined by calculating the tie differential between the oints at which the stave assed the bea when travelling in the sae direction. hat is, the tie differential was calculated between every second ulse and at the sae oint on the ulse signal: the instant that the ulse occurred. 36

47 DSO-N-140 Roll Frae (Bea Breaker) Power Suly (10v DC) Laser Encoder BNC Interface LabView DAQ Device HP Deskto PC (LabView Software) Figure B3 Digital laser encoder tie easureent syste: syste architecture block diagra. Reflector Dynaic Frae Bea Breaker Laser Encoder Static Frae Figure B4 Digital laser encoder tie easureent syste: hysical setu. 37

48 DSO-N-140 Run A10 Voltage [v] Pre-test Initial Angle Set Free Oscillation of Dynaic Frae ie [sec] Figure B5 Digital laser encoder tie easureent syste: recorded voltage signal. he existing AMC standard oerating rocedure was executed for the frae setu and test rocess using the ontoon odel. wo oerators were used to easure and record the oscillation tie using the anual stowatch ethod. en consecutive oscillations were counted in each of the tests. he laser encoder syste was oerated siultaneously to record the voltage signal during these tests. his rocess was followed for the 10 and 15 degree initial angle tests. A 5 degree initial angle test was atteted; however, due to the daing in the roll frae syste, the nuber of colete oscillations did not reach the iniu requireent of ten full oscillations. Each test was reeated five ties to investigate the reeatability of the test rocess. he test araeters and the results of the 10 degree and 15 degree tests are resented below. est Paraeters for AMC-03-10: = kg (odel ass) = kg (endulu ass) h = (distance that the endulu ass was dislaced) 38

49 DSO-N-140 able B1 10 degree initial heel angle oscillation tie easureents. Run Descrition Sto Watch No. 1 (10 oscillations) [sec] Sto Watch No. (10 oscillations) [sec] Sto Watch Average Period [sec] Laser Encoder [sec] Model & Frae Model & Frae Model & Frae Model & Frae Model & Frae AVERAGE SDEV Frae Only Frae Only Frae Only Frae Only Frae Only AVERAGE SDEV able B 15 degree initial heel angle oscillation tie easureents. Run Descrition Sto Watch No. 1 (10 oscillations) [sec] Sto Watch No. (10 oscillations) [sec] Sto Watch Average Period [sec] Laser Encoder [sec] Model & Frae Model & Frae Model & Frae Model & Frae Model & Frae AVERAGE SDEV Frae Only Frae Only Frae Only Frae Only Frae Only AVERAGE SDEV he roll gyradius was calculated using Equation with the easured test araeters. A general uncertainty analysis was also coleted for each of the test configurations using Equation 6. he results are resented in able B3 and Figure B6. Uncertainty estiates in easured araeters: U = kg U h = 0.00 U = kg 10 degree initial angle U 1 = sec (stowatch) 39

50 DSO-N-140 U = sec (stowatch) U 1 = sec (Laser encoder) U = sec (Laser encoder) 15 degree initial angle U 1 = 0.05 sec (stowatch) U = sec (stowatch) U 1 = 0.00 sec (Laser encoder) U = sec (Laser encoder) able B3 Roll gyradius calculation results and uncertainty estiates (95% confidence level). Run Descrition Roll Gyradius [] Uncertainty [] Uncertainty [%] Sto Watch (10 deg) ± 3.10 x Laser Encoder (10 deg) ± 4.70 x Sto Watch (15 deg) ±.7 x Laser Encoder (15 deg) ± 4.35 x Stowatch Laser Encoder Roll Gyradius (k ) [] Initial Angle [deg] Figure B6 Roll frae test results of roll gyradius versus initial angle for the stowatch and laser encoder easureent ethods. he ean and standard deviation of all four easureents are μ = and σ = 9.57x10-4. he results of the roll frae tests indicate the following outcoes: 1. he laser encoder syste has a significantly higher recision than the anual stowatch ethod; however, the absolute values of the roll gyradius deterined using the two ethods are not significantly different. 40

51 DSO-N-140. U to an initial angle of 15 degrees, there is no discernable effect caused by the initial angle on the easured araeters and roll gyradius. 3. he daing in the roll frae syste is of a agnitude that is significant enough to require at least an initial angle of 10 degrees to achieve 10 oscillations when conducting a test using the sall roll frae. B.. Coarison with CAD Method As discussed in B.1, the geoetry of the ontoon odel was odelled using the Rhinoceros 3D CAD software rogra. he ontoon was odelled as a series of solid eleents based on a etrological survey conducted by the author. he hysical odel is anufactured with a lywood substrate covered externally with a fibreglass lainate and internally with an eoxy lacquer. he internal stiffeners are glued to the external anels and are only covered with the eoxy lacquer. Desite the relative difference in the density of the aterials and coatings, the CAD odel is an isotroic reresentation of the hysical geoetry of the ontoon. he volue roerties of the odel were calculated using the VolueMoents function with all of the solid objects selected. he volue oent data returned by Rhinoceros 3D and relevant to this study are suarised in able B4 below. hese values are stated relative to the odel s geoetric centre of volue. able B4 Rhinoceros 3D calculated volue oent data. Calculated Proerty Calculated Value Calculated Error Cuulative Volue [ 3 ] ± 1.60 x 10-8 Volue Moent About Centroid (I x) [ 5 ] 4.75 x 10-4 ± 1.60 x 10-9 Volue Gyradii About Centroid (k ) [] ± 3.70 x 10-7 Longitudinal Volue Centroid (XCG) [] ± 1.0 x 10-6 ransverse Volue Centroid (YCG) [] x 10-6 ± 8.80 x 10-9 Vertical Volue Centroid (ZCG) [] ±.70 x 10-7 Based on the results resented in able B3 and able B4 there is a 1.0 ercent difference between the ean roll gyradius value easured using the roll frae and the roll gyradius calculated using the CAD ethod. Considering the uncertainties in the hysical easureent and the assutions of hoogeneity and isotroy in the CAD odel, this result indicates that the roll frae has rovided an accurate easureent of the roll gyradius for the ontoon odel in air. B.3. Design Issues he AMC currently oerates two roll frae devices to easure the roll gyradius of odel arine craft and offshore structures. A larger roll frae exists in addition to the sall roll frae evaluated in this investigation. he requireent to have two roll fraes is driven by the overall size of the odel being tested. o date, the oerators have noted several otential issues that ay influence the roll gyradius easureent [15]. hese issues are: 41

52 DSO-N he deflection of the dynaic frae s longitudinal beas due to the weight of the odel and the resulting isalignent of the roll frae axis of rotation and the odel s vertical centre of ass.. Misalignent of the shaft axes, indeendent of loading, which ay introduce excessive friction daing and liit the duration of oscillation. hese issues have been investigated, albeit at a cursory level, to verify their otential for introducing error into the roll frae roll gyradius easureent syste. A finite eleent structural analysis was coleted for the sall and large roll fraes to quantify the effect of odel weight on the deflection of the dynaic frae sub-assebly. he analysis and results are resented in B.3.1. A qualitative evaluation of the bearings has been coleted and alternative otions are resented in B.3.. B.3.1 Misalignent due to structural deflection A linear structural finite eleent (FE) analysis of the dynaic frae sub-assebly was coleted using the Maestro V FE analysis software [16] for both the sall and large roll fraes used by the AMC. In both cases, the dynaic frae geoetry was odelled and eshed using Rhinoceros 3D and Maestro. he dynaic frae was odelled using shell eleents only. Restraints were laced on the frae at the location of the axis of rotation on each transverse bea. he frae was restrained such that no vertical (z) or longitudinal (x) translation or rotation was eritted. Four oint loads were laced at the location of the underslung suorts in their innerost location. Each oint load carries one quarter of the total alied load. he Maestro esh generated for the sall roll frae is resented in Figure B7. he esh contains 1385 nodes and 1350 triangular eleents and is relatively coarse. he aterial roerties assigned to the structural odel are resented in able B5. 4

53 DSO-N-140 Z Y X Figure B7 AMC sall roll frae: dynaic frae FE esh geoetry, oint loads (red arrows) and restraints (green arrows). able B5 Material roerties assigned to the sall roll frae FE odel. Proerty Value Material Aluiniu Wall thickness of SHS 1.50 Young s Modulus of Elasticity 70 GPa Poisson s Ratio 0.33 A load versus deflection analysis was coleted for the sall roll frae for odel weights of between 10 kilogras and 100 kilogras inclusive. he FE analysis results indicate that the location of axiu deflection (and absolute dislaceent) occurs at the id-san of the longitudinal beas (Figure B8). his is also the location of the axiu cobined stress (Figure B9). he load versus deflection results for the sall roll frae is resented in able B6. he results indicate that there is negligible deflection in the frae for odels weighing u to 50 kilogras. At loads above 50 kilogras the aount of deflection and isalignent begins to exceed the accetable anufacturing tolerances that are alied to hysical odel itself. he IC rescribes a axiu diensional anufacturing tolerance of ±1.00 illietre [17]. It is in this region where the isalignent of the odel s centre of ass and the roll frae roll axis could introduce easureent errors in the araeters used to calculate the odel s roll gyradius. 43

54 DSO-N-140 able B6 AMC sall roll frae: odel weight versus longitudinal bea axiu deflection. Model Weight [kg] Longitudinal Bea Maxiu Deflection [] Z Y X Figure B8 Bea deflection due to four oint loads and a odel ass of 60kg. he original (unloaded) frae osition is reresented by the array of arkers. he dislaceent is scaled by a factor of 100. In this condition the axiu dislaceent is 1.10 illietres and occurs at the id-san of the two longitudinal beas. 44

55 DSO-N-140 Z Y X Figure B9 Colour a of the Von Mises cobined stress distribution due to four oint loads and a odel ass of 60kg. he original (unloaded) frae osition is reresented by the array of arkers. he FE esh odel of the large roll frae s dynaic frae assebly is substantially finer than that develoed for the sall roll frae. his is sily due to the geoetry discretization rocess used to achieve eleents with an asect ratio as close to unity as ossible. he odel corises 4316 nodes and 498 quadrilateral eleents. he aterial roerties of the large roll frae s structural sections, and those used in the FE analysis, are the sae as the sall roll frae (able B5). he axiu odel length and breadth that can be accoodated by the large roll frae is.5 etres and 0.75 etres, resectively. A load versus deflection analysis was coleted for the large roll frae for odel weights of between 0 kilogras and 10 kilogras inclusive. he FE analysis results indicate that, siilar to the sall roll frae, the location of axiu deflection occurs at the id-san of the longitudinal beas (Figure B10). his is also the location of the axiu cobined stress (Figure B11). he load versus deflection results for the sall roll frae is resented in able B7. he results indicate that even for a odel of 0 kilogras, the deflection exceeds the axiu diensional tolerance for odel anufacture. For a odel weight of 10 kilogras the deflection in the longitudinal bea is significant (5.36 illietres over a san of 1310 illietres). It is very likely that the deflection of the longitudinal beas and the resulting isalignent of the odel s centre of ass and the roll frae roll axis will introduce non-negligible easureent errors in the easureent of the odel s roll gyradius. 45

56 DSO-N-140 Z Y X Figure B10 Large roll frae dynaic frae assebly: bea deflection due to four oint loads and a odel ass of 10 kg. he original (unloaded) frae osition is reresented by the array of arkers. he dislaceent is scaled by a factor of 100. In this condition the axiu dislaceent is 5.36 illietres and occurs at the id-san of the two longitudinal beas. Z Y X Figure B11 Large roll frae dynaic frae assebly: colour a of the Von Mises cobined stress distribution due to four oint loads and a odel ass of 10 kg. he original (unloaded) frae osition is reresented by the array of arkers. he dislaceent is scaled by a factor of

57 DSO-N-140 able B7 AMC sall roll frae: odel weight versus longitudinal bea axiu deflection. Model Weight [kg] Longitudinal Bea Maxiu Deflection [] As discussed in 4.1.1, it is iortant to aintain a very light dynaic frae in order to axiise the difference in the oents of inertia of the frae only and frae with odel test configurations to iniise the uncertainty in the easureent of the roll gyradius. Achieving this weight requireent and aintaining the structural integrity of the frae is considered to be a challenging design roble and one that ust be addressed through aterial selection and/or structural arrangeent. his task is beyond the scoe of this investigation. Furtherore, the FE analyses resented in this reort are considered to be of a reliinary level. It would be rudent to conduct ore detailed analyses that give consideration to the dynaic loads acting on the entire roll frae syste when in oeration. Nonetheless, the reliinary FE analysis results rovide evidence that the dynaic frae and odel will be isaligned under noral oerating conditions. B.3. Shaft and Bearing Misalignent In general ters, shaft and bearing isalignent, whether angular or arallel, will result in dysfunctional oeration and unnecessary wear. While soe bearing tyes can accoodate sall levels of angular isalignent, the isalignent of the shaft is the critical issue in the case of the roll frae. Moreover, the freedo of the bearing to accoodate isalignent acts in oosition to aintain recise shaft alignent. he two ajor oerational dysfunctions that result due to shaft isalignent are: 1. he centre of ass of the odel is not aligned with the roll frae s axis of rotation.. here is an increase in the syste daing which affects the oerability of the roll frae Deending on the severity of the shaft isalignent, these dysfunctions will directly affect the easureent of the roll eriods ( 1 and ) and the consequently, the roll gyradius (k ). he sall roll frae s shaft and bearing arrangeent is shown in Figure B1. 47

58 DSO-N-140 Figure B1 KML ounted flange bearing and shaft arrangeent connecting the static and dynaic frae sub-asseblies. An alternate design solution and one that has been used in a siilar alication is the knife edge ounting arrangeent shown in Figure B13. If integrated effectively, the knife edge arrangeent results in a durable couling that will allow the dynaic frae to rotate about its longitudinal axis with inial friction losses. Referring to Figure B1, the vertical (z-z), lateral (y-y) and yaw (rotation about z-z) alignent of the knife edge axes is achieved by aligning the knife edge and seat coonents at both ends of the roll frae. Rotation about the y-y axis (the condition where the knife edge and seat break contact with each other) is liited by the weight of the frae and the structural rigidity inherent in a sufficiently well designed seat and dynaic sub-assebly. Figure B13 Knife edge ounting arrangeent resented by Miller [18]. 48