validation of ship motion predictions with sea trials data

25th Symposium on Naval HydrodynamicsSt. Johns, Newfoundland and Labrador, CANADA, 8-13 August 2004

Validation of Ship Motion Predictions with Sea Trials

Data for a Naval Destroyer in Multidirectional Seas

Kevin McTaggart and Dave Stredulinsky(Defence R&D Canada - Atlantic, Canada)

ABSTRACT

This paper presents comparisons of ship motionpredictions with measured motions for the Cana-dian naval destroyer HMCS Nipigon in seaways withsignificant wave heights ranging from 3.7 m to 5.8 m.The numerical predictions include modelling of en-countered directional seaways, which were measuredby a directional wave buoy. Motions were predictedusing a strip theory code and with DRDC Atlantic’snew ShipMo3D library, which uses a panel methodbased on the frequency domain Green function forzero forward speed. To investigate the influence ofappendages on radiation forces, frequency domaincomputations included treatment of the combinedpanelled hull and panelled appendages. Time do-main computations were performed for both linearand nonlinear evaluation of hull forces due to buoy-ancy and incident waves. Agreement between pre-dicted and observed RMS motions and zero-crossingperiods is generally good. Differences between re-sults from the five different sets of predictions arerelatively minor.

INTRODUCTION

Predictions of ship motions in waves are being usedby navies for a widening number of applications. Inthe past, ship motion predictions have been usedprimarily for engineering design applications. Inrecent years, there has been increasing interest inship motion predictions by naval operators due tothe influence of ship motions on safety and oper-ational effectiveness. Search and rescue missionsand ship-borne helicopter operations are examples

where ship motions must be duely considered. Shipmotions also influence the effectiveness of crew, wea-pon systems, and sensor systems. The recent trendtoward large-scale simulations of military systemsis creating increased demand for modelling of shipmotions and their influence on ship systems. De-pending on simulation requirements, appropriatetrade-offs must be made between computational re-quirements and prediction fidelity.

To address ongoing requirements for shipmotion predictions, DRDC Atlantic is developingthe ShipMo3D library for simulation of ship mo-tions and sea loads in waves. The library includesmodules for computations in both the frequencyand time domains. For time domain computations,nonlinear computations of buoyancy and incidentwave forces are available. To meet requirementsof military simulation applications, it is intendedthat computations be available that can run fasterthan real-time without significantly compromisingprediction fidelity.

Validation with experimental data is an es-sential part of development of any ship motion pre-diction code. When considering the relative mer-its of model tank tests and full-scale trials, modeltank tests typically have the advantages of lowercosts, greater control over encountered conditions,and completeness of data. However, full-scale trialsare considered essential because they include phe-nomena that can be absent in model tests due tooversight or scaling effects. Consequently, both full-scale trials and model tests are recommended forvalidation of numerical ship motion predictions. Tosupport ongoing validation efforts, DRDC typicallyconducts one or two sea trials per year measuring

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ship motions and sea loads in waves. The trials areusually held off the coast of Nova Scotia in the win-ter months, when rougher sea conditions are morelikely to occur. This paper describes the validationof ship motion predictions with sea trial data forthe destroyer HMCS Nipigon.

OVERVIEW OF SHIPMO3DLIBRARY FOR PREDICTINGSHIP MOTIONS IN WAVES

DRDC Atlantic has been an active developer, user,and sponsor of codes for predicting ship motionsand sea loads since the 1970s. Several differentcodes are currently used, with each code havingits own particular strengths and weaknesses. Thein-house strip theory code SHIPMO7 (McTaggartet al. 1997, McTaggart 2000) was originally devel-oped by Schmitke (1978) and has a large user base.Other codes for which DRDC Atlantic has been aco-sponsor are used when time domain predictionsare required or when three-dimensional hydrody-namic effects are important.

The ShipMo3D library is an effort to con-solidate ship motion prediction capabilities into aunified entity that will satisfy a range of applicationrequirements. ShipMo3D uses a panel method toprovide enhanced accuracy relative to strip theory,and to ensure applicability to the range of vesselsoperated by the Canadian Navy. Hydrodynamiccoefficients are computed in the frequency domainbased on the Green function for zero forward speed,similar to approaches presented by Beck and Lo-ken (1989) and Papanikolaou and Schellin (1992).The decision to use this method was based partlyon the relatively slow speeds of present and antic-ipated Canadian naval vessels, which operate atFroude numbers less than 0.4. Other considera-tions included computational efficiency and robust-ness relative to methods using non-zero forwardspeed Green functions in either the time or fre-quency domains. Comparisons with experimentspresented by McTaggart et al. (1997) and Schellinet al. (2002) indicate that the zero forward speedGreen function can lead to very good motion andsea load predictions at moderate ship speeds.

The ShipMo3D library provides motion pre-dictions in both the frequency and time domains.For time domain predictions, hydrodynamic coef-ficients, including retardation functions, are deter-

mined from previously computed frequency domainvalues, similar to the approach used by Ballard etal. (2003). Comparisons of hydrodynamic forcesand motions for the frequency and time domainshave verified correct prediction of time domain co-efficients from frequency domain coefficients.

Motions are currently computed for a shiptravelling at nominally steady speed and heading.Motion computations are performed using a trans-lating earth axis system. Nonlinear buoyancy andincident wave forces can be evaluated based on theinstantaneous wetted surface. Nonlinear buoyancyand incident wave forces are initially computed ina ship-fixed axis system and then rotated to thetranslating earth axis system. Other hydrodynamicforces (i.e., added mass, retardation, and wave dif-fraction) are assumed to maintain their translatingearth axis system values regardless of large ampli-tude ship motions.

SHIPMO3D APPENDAGE FORCEPREDICTIONS

Sway, roll, and yaw motions are significantly in-fluenced by appendage forces. In addition, viscousforces acting on the ship hull make a noticeable con-tribution to roll damping. These forces are mod-elled in ShipMo3D based on approaches presentedby Schmitke (1978) and Himeno (1981). Unfortu-nately, roll motions continue to present a significantchallenge for ship motion codes due to difficultiesin predicting roll damping components.

When examining methods for predictingviscous roll damping components, there is greatvariability in predicted values for bilge keel dragforces. The viscous roll moment acting on a bilgekeel can be expressed as:

F bk−v4 =

12

ρ η̇24

∫ xfore

xaft

Cd(x) s(x) r̃3BK(x)dx (1)

where ρ is water density, η̇4 is roll velocity, xaft

and xfore are the aft and forward longitudinal co-ordinates of the bilge keel, Cd(x) is the local dragcoefficient, and s(x) is the local span. The effectivecube of the local viscous roll moment arm, r̃3

v(x), isgiven by:

r̃3BK(x) = r3

BK(x) (y cos Γ + z sin Γ)2 (2)

where rBK(x) is the radius from the local bilge keelcenter to the ship center of gravity (CG), y is the

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lateral coordinate (+ port) relative to the ship CG,Γ is the dihedral angle of the bilge keel relative tohorizontal (+ upward), and z is the vertical coordi-nate (+ upward) relative to the ship CG. Neglect-ing hull interaction and free surface effects, a longflat plate normal to flow will have a drag coefficientof approximately 1.2. In contrast, bilge keel dragcoefficients given by Lloyd (1989) vary between 2and 12, with the upper value occurring for smallamplitude roll motions.

DRDC Atlantic’s strip theory code SHIP-MO7 models bilge keel viscous drag using the ap-proach described by Schmitke (1978) based on thework of Kato (1966). Kato’s formulation is quitecomplicated, but can be simplified to the followingfor a representative destroyer:

Cd(x) ≈ 5

(rBK(x) η̂4 ωe√

g s(x)

)−0.6

×[1.0 + 3.5 exp

(−11Rbilge(x)

rBK(x)

)](3)

where Rbilge(x) is the local bilge radius of the hull,η̂4 is roll amplitude, and ωe is wave encounter fre-quency. Perhaps the most noteworthy feature ofEquation (3) is the large degree of variation of thedrag coefficient with roll velocity amplitude η̂4 ωe.When considering Equations (1) and (3) together,the proportionality of viscous roll drag to (η̂4 ωe)1.4

combined with the presence of gravitational accel-eration in Equation (3) possibly arise from trying tomodel radiation and viscous forces simultaneously.

The ShipMo3D library currently models thebilge keel drag coefficients as follows:

Cd = Cd−ref (̂̇η4−ref )

( ̂̇η4̂̇η4−ref

)−α

(4)

where Cd−ref is an input reference drag coefficientfor roll velocity amplitude ̂̇η4−ref and α is an inputdecay exponent. This approach provides flexibil-ity in the selection of bilge keel roll damping co-efficients, including the possibilities of using inputvalues from experiments or CFD computations.

Appendage force predictions by Schmitkeneglect free-surface effects. The influence of thehull on appendage potential flow forces is mod-elled by assuming that the local hull is a planarboundary. The influence of the appendages on hullforces is neglected. The ShipMo3D library intro-duces an option for including appendages in hull

radiation and diffraction computations by assum-ing that appendages are thin and modelling themusing dipole panels (Chakrabarti, 1987). Due tothe significant variation of dipole strengths acrossa flat plate (Meyerhoff, 1970), each appendage typ-ically has several panels in each of the span-wiseand chord-wise directions.

NAVAL DESTROYER HMCSNIPIGON

The naval destroyer HMCS Nipigon (Figure 1) wasthe subject of a comprehensive sea trial measur-ing ship motions and sea loads in December 1997.HMCS Nipigon was the last steam-driven destroyerin the Canadian Fleet. Figure 2 gives a body planfor Nipigon and Table 1 gives particulars. Nipigonappendages include 2 rudders, 2 outer propellershaft brackets, 2 inner propeller shaft brackets, 2bilge keels, and a skeg, with dimensions as given inTable 2.

Figure 1: HMCS NIPIGON

SEA TRIAL ON HMCS NIPIGON

During the December 1997 sea trial, a series of 71trial runs of 20 to 30 minute duration was under-taken at two nominal ship speeds in head, bow,beam, quartering and following seas. Data werecollected in higher sea states (4, 5 and 6) for threedays over December 2, 3 and 4th and for four daysat lower sea states (2 and 3) over December 8 to11th. The ‘low’ ship speed was about 8 knots and

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Figure 2: Body Plan for HMCS Nipigon

Table 1: Particulars for HMCS Nipigon

Displacement 3027 tonnesLength between perpendiculars 108.4 mBeam 12.8 mDraft 4.3 mTrim by stern 0.5 mHeight of CG above keel 5.1 mCG from forward perpendicular 57.5 mBlock coefficient 0.503Prismatic coefficient 0.625Wetted hull area 1446 m2

Metacentric height 1.2 mRoll radius of gyration 5.6 mPitch radius of gyration 27.1 mNatural roll period 10.6 s

Table 2: Appendages for HMCS Nipigon

Rudders (2)Station 19.3Root lateral offset 1.981 mRoot above baseline 3.197 mSpan 3.023 mRoot chord 2.286 mTip chord 1.886 mDihedral angle (port) -90 degArea (port+starboard) 12.6 m2

Outer shaft brackets (2)Station 18.3Root lateral offset 3.109 mRoot above baseline 3.200 mSpan 2.256 mRoot chord 0.800 mTip chord 0.800 mDihedral angle (port) -99.5 degArea (port+starboard) 3.6 m2

Inner shaft brackets (2)Station 18.3Root lateral offset 1.158 mRoot above baseline 2.957 mSpan 2.240 mRoot chord 0.800 mTip chord 0.800 mDihedral angle (port) -64.2 degArea (port+starboard) 3.6 m2

Bilge Keels (2)Fore station 8.82Aft station 13.79Span 0.610 mArea (port+starboard) 32.9 m2

Skeg at CenterlineFore station 14.0Aft station 16.5Aft span 1.236 mArea 6.8 m2

Station 20 is aft perpendicular

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‘high’ ship speed was between 14 and 18 knots de-pending on what speed the ship could maintain inthe given sea state. Speed was limited due to theloss of one of the two ship boilers on the first dayof the trial.

Trial instrumentation included a ship mo-tions package, a wave buoy, a TSK over-the-bowwave height meter, an array of 24 pressure trans-ducers outfitted in the hull below the waterline, 15single strain gauges, and 4 rosette strain gauges.Wave data were collected for 20 minutes out ofevery hour from the wave buoy. An Endeco type1156 directional wave buoy was used for the first3 days of the trial, and a type 956 buoy was usedfor the last 4 days. Figure 3 shows an Endeco wavebuoy being deployed from Nipigon. The main dataacquisition system was a PC-based LabVIEW sys-tem. All sixty instrumentation channels were digi-tally sampled at 20 Hz. Time histories, statisticaldistributions and minimum and maximum valueswere determined and recorded.

For the present study only the ship motionand wave data have been used. A limited numberof runs from the first three days of the trial wasselected to satisfy the following 3 criteria:

• the significant wave height Hs was greaterthan 3 m,

• there was a clear dominant wave direction andminimal directional wave spreading,

• the nominal relative wave direction was oblique(bow quartering, beam, or stern quarteringseas).

Table 3 gives a summary of the runs selected forthe present study, with Tz denoting zero-crossingwave period. Figure 4 shows an example measuredwave spectrum.

Rudder deflections were not measured dur-ing the sea trial, and are assumed to have had noeffect on ship roll motions. In reality, the ruddermotions could have significantly influenced the shiproll motions, particularly if rudder motions wereat a frequency similar to the ship natural roll fre-quency.

Figure 3: Endeco Wave Buoy Being Deployed fromHMCS Nipigon

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Table 3: NIPIGON Trial Runs Used in PresentStudyRunSpeed Hs Tz Wave dir. Ship Rel.

(kt) (m) (s) (from, deg) head. waveMean Dev. (to, deg) head.

203 8 3.73 7.73 218 39 265 BQ204 8 3.67 7.21 225 39 85 SQ206 16 3.89 7.39 228 25 355 SQ209 13 4.75 8.07 224 33 265 BQ210 15 4.75 8.07 224 33 85 SQ303 8 5.82 9.45 274 41 310 BQ304 8 5.57 8.81 272 39 120 SQ305 8 5.57 8.81 272 39 220 BQ306 8 5.16 8.66 266 45 50 SQ309 14 5.39 8.95 279 32 315 BQ310 14 5.44 8.73 269 43 135 SQ403 8 5.01 9.34 244 40 290 BQ404 8 4.90 9.60 238 47 110 SQ409 16 4.52 8.37 238 50 285 BQ410 16 4.52 8.37 238 50 105 SQ413 8 4.98 8.86 245 40 330 BmRelative wave headingsBQ - Bow quarteringSQ - Stern quarteringBm - Beam

Contours at 10, 20, 40, 60, and

80 % of peak: 0.72 m2/(Hz-deg)

1010

0

90

180

270

0.05

0.1

0.15

0.2 Hz

Figure 4: Measured Directional Wave Spectrum forRun 203

NUMERICAL PREDICTIONS OFSEA TRIAL MOTIONS

Numerical predictions of ship motions during seatrial runs were made using the strip theory programSHIPMO7 and with the ShipMo3D library.

All predictions considered the ship motionsin the measured short-crested seaways. Four dif-ferent types of predictions were made using theShipMo3D library:

• frequency domain predictions, appendages notincluded in hull radiation and diffraction com-putations,

• frequency domain predictions, both hull andappendages included in radiation and diffrac-tion computations,

• time domain predictions with linear buoyancyand incident wave forces,

• time domain predictions with nonlinear buoy-ancy and incident wave forces.

The time domain predictions do not include the ap-pendages in the hull radiation and diffraction com-putations.

For three-dimensional radiation and diffrac-tion computations, the wet hull was represented by814 flat panels (407 panels on the port side), withmost panels being quadrilaterals and the remainderbeing triangles. The dry hull, required for comput-ing nonlinear buoyancy and incident wave forces,was represented by a total of 1,276 panels. Fig-ure 5 shows the panelled hull, with the wet portionrepresented by white panels and the dry portionrepresented by grey panels. For radiation and dif-fraction computations including panelling of the ap-pendages, the port and starboard appendages weremodelled using 308 panels (154 panels on the portside), and the centerline skeg was modelled using18 panels. Figure 6 shows the port half of the hullin red, and appendages on the port side and cen-terline in yellow. Figure 7 shows expanded views ofthe panelled aft appendages.

Hydrodynamic coefficients in the frequencydomain were computed at the zero and infinite fre-quency limits and at intermediate encounter fre-quencies of 0.1, 0.2, . . ., 6.0 rad/s. For each en-counter frequency, computed terms include the zero

6

Figure 5: Nipigon Wet (White) and Dry (Grey)Panelled Hull

Figure 6: Aft Portion of Nipigon Wet Panelled Hull(Red) with Appendages (Yellow)

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Bilge keel

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Skeg

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Inner bracket

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Outer bracket

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Rudder

Figure 7: Profiles of Nipigon Panelled Appendages

speed coefficients and terms proportional to shipspeed U and U2 that can be used to evaluate hy-drodynamic coefficients at arbitrary forward speed.Wave diffraction terms were evaluated for speeds of0, 5, . . ., 30 knots, relative wave directions of 0, 10,. . ., 180 degrees, and wave frequencies of 0.2, 0.3,. . ., 2.0 rad/s. The computed hydrodynamic coef-ficients and diffraction forces form a database fromwhich hydrodynamic forces can be obtained for anyseaway encountered by the ship.

For time domain simulations, retardationfunctions were computed using convolution inte-grals applied to previously computed frequency do-main coefficients. The retardation functions werecomputed for delay times of 0.0, 0.1, . . ., 20 s. Re-tardation forces are negligible beyond delay timesof 20 s. Time domain simulations were conductedusing both linear and nonlinear forces from buoy-ancy and incident waves. For nonlinear incidentwave forces, Wheeler stretching (Wheeler, 1970)was used to model the variation of velocity poten-tial with distance below the instantaneous free sur-face. The time domain simulations used a time stepsize of 0.2 s and total duration of 30 minutes.

The bilge keel roll damping was modelledusing Equation (4) with a reference drag coefficientof 16.5 for the ship rolling with an amplitude of 5degrees at its natural roll period of 10.6 s. The de-cay coefficient α has a value of 0.60. Both the ref-erence drag coefficient and decay coefficient wereobtained from calculations using Kato’s method.Figure 8 shows the variation of bilge keel drag co-efficient with roll amplitude for oscillations at theship natural roll frequency. During time domaincomputations, it was necessary to select a nomi-nal roll velocity amplitude for computing the bilgekeel drag coefficient. At each time step, the nom-inal roll velocity amplitude was set to 1.25 timesthe RMS roll velocity during the most recent 20 sof motion. All other appendages were assumed tohave constant drag coefficient values of 1.17.

Time domain simulations with the Ship-Mo3D library currently are limited to a ship withnominally steady speed and heading. Due to theabsence of rudder motion data during the sea trial,rudder motions were assumed to be small. Thisassumption will have little influence on predictedroll motions if the rudder motions were limited tolow frequency. To ensure course-keeping, additionalstiffness and damping terms given in Table 4 wereused for surge, sway, and yaw. The stiffness and

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0 10 20

Roll amplitude η̂4 (deg)

0

10

20

30

40

50D

rag

coeffi

cien

tC

d............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................

Figure 8: Bilge Keel Drag Coefficient Versus RollAmplitude at Ship Natural Roll Period of 10.6 s

damping values were selected such that they wouldhave only a minor influence on predicted motions,and are based on natural periods of approximately100 s and damping of approximately half of criticaldamping.

Table 4: Additional Stiffness and Damping for En-suring Course-Keeping with ShipMo3D Computa-tions

Stiffness DampingSurge 1 × 104 N/m 2 × 105 N/(m/s)Sway 2 × 104 N/m 4 × 105 N/(m/s)Yaw 2 × 108 Nm/rad 2 × 108 Nm/(rad/s)

Due to strong roll resonance behavior, itis essential that sufficiently fine increments be usedfor wave frequency and wave direction. The com-putations in both the frequency and time domainsused incident seaway components with wave fre-quencies of 0.2, 0.25, . . ., 2.0 rad/s and absolutewave directions of 0, 10, . . ., 360 degrees. For mea-sured directional sea spectra, the number of non-zero wave spectral components within the specifiedcombinations of wave frequency and wave directionranged from 158 to 323.

For the time domain computations usinglinear buoyancy and incident wave forces, computa-tional times were approximately three times fasterthan real-time on an 800 MHz Pentium III desktopcomputer. When nonlinear buoyancy and incidentwave forces were evaluated at each time step on

the instantaneous wetted hull, computational timeswere approximately one third as fast as real-time.

COMPARISONS OF SEA TRIALDATA AND PREDICTIONS

Tables 5 to 10 give observed and predicted val-ues of RMS displacements and zero-crossing peri-ods for heave, roll, and pitch. Agreement betweenobserved and predicted values is generally good,with the best agreement occurring for heave, fol-lowed by pitch and roll, respectively. The five dif-ferent prediction methods give quite similar results.Figures 9 to 14 show scatter plots of predicted ver-sus observed RMS motions and zero-crossing peri-ods, where the predictions are from time domainsimulations with nonlinear buoyancy and Froude-Krylov forces.

INFLUENCE OF APPENDAGEFORCE PREDICTIONS ON ROLLHYDRODYNAMICS

The frequency domain predictions presented in Ta-bles 5 to 10 indicate that including the panelledappendages in radiation and diffraction computa-tions has very little influence on predicted hydro-dynamic forces for Nipigon. Figures 15 and 16 showroll added mass and damping versus ship speed formotions at Nipigon’s natural roll period of 10.6 s.Added mass is non-dimensionalized by ship roll in-ertia I44, and damping is non-dimensionalized bycritical roll damping at zero speed Bcr

44. Results aregiven for zero amplitude roll motions (i.e., viscousroll forces are negligible). Figure 15 indicates thattreating the appendages separately from the hullgives slightly higher added mass than when usingpanelled appendages integrated with the hull ra-diation computations. As expected, the bare hullhas lower added mass than the appended hull. Fig-ure 16 shows that including the panelled appendagesin the radiation computations has negligible effecton predicted roll damping, with the relevant plot-ted lines being indistinguishable.

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Table 5: Observed and Predicted RMS Heave (m)Run Trial Strip 3D freq. 3D time

theory Appendages Hull forcesSep. Integ. Linear Nonlin.

203 0.70 0.65 0.66 0.66 0.68 0.68204 0.55 0.48 0.47 0.47 0.46 0.46206 0.76 0.60 0.58 0.58 0.59 0.59209 0.84 0.90 0.96 0.96 0.99 1.00210 0.89 0.71 0.67 0.67 0.68 0.68303 1.38 1.10 1.11 1.11 1.01 1.00304 1.02 0.93 0.90 0.90 0.80 0.80305 0.98 1.19 1.19 1.19 1.17 1.17306 0.81 0.97 0.95 0.95 1.00 1.00309 1.33 1.07 1.12 1.11 1.12 1.13310 0.97 0.92 0.89 0.89 0.88 0.88403 1.15 1.00 1.01 1.00 1.05 1.05404 0.88 0.93 0.92 0.92 0.89 0.89409 1.13 0.88 0.94 0.94 0.96 0.97410 0.78 0.74 0.72 0.72 0.72 0.72413 1.09 1.14 1.15 1.15 1.13 1.13Predicted/observedMean 0.94 0.94 0.94 0.93 0.94Deviation 0.14 0.14 0.14 0.15 0.16

Table 6: Observed and Predicted Heave Zero-Crossing Period (s)Run Trial Strip 3D freq. 3D time



Table 7: Observed and Predicted RMS Roll (deg)Run Trial Strip 3D freq. 3D time



Table 8: Observed and Predicted Roll Zero-Crossing Period (s)Run Trial Strip 3D freq. 3D time



9

Table 9: Observed and Predicted RMS Pitch (deg)Run Trial Strip 3D freq. 3D time



Table 10: Observed and Predicted Pitch Zero-Crossing Period (s)Run Trial Strip 3D freq. 3D time



0.0 0.5 1.0 1.5

Observed RMS Heave (m)

0.0

0.5

1.0

1.5

Pre

dic

ted

RM

SH

eave

(m)

Relative heading+ Bow quartering• Beam◦ Stern quartering

..........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................

+

+ +

++

++

•

◦◦

◦◦

◦◦◦

◦

Figure 9: Predicted Versus Observed RMS Heave,Time Domain Predictions with Nonlinear Buoy-ancy and Incident Wave Forces

0 5 10 15

Observed Tz Heave (s)

0

5

10

15

Pre

dic

ted

Tz

Hea

ve(s

)


..........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................

+

+

+

++

+

+

•

◦ ◦

◦◦

◦

◦◦◦

Figure 10: Predicted Versus Observed Heave Zero-Crossing Period, Time Domain Predictions withNonlinear Buoyancy and Incident Wave Forces

10

0 2 4 6 8

Observed RMS Roll (m)

0

2

4

6

8

Pre

dic

ted

RM

SRoll

(deg

)


..........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................

++

++

+

+

+

•

◦

◦◦

◦

◦

◦◦◦

Figure 11: Predicted Versus Observed RMS Roll,Time Domain Predictions with Nonlinear Buoy-ancy and Incident Wave Forces

0 5 10 15

Observed Tz Roll (s)

0

5

10

15

Pre

dic

ted

Tz

Roll

(s)


..........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................

++

+++

++•◦ ◦

◦◦◦

◦

◦

◦

Figure 12: Predicted Versus Observed Roll Zero-Crossing Period, Time Domain Predictions withNonlinear Buoyancy and Incident Wave Forces

0 1 2

Observed RMS Pitch (m)

0

1

2

Pre

dic

ted

RM

SPitch

(deg

)


..........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................

+

+

+ +

+

++

•

◦ ◦

◦ ◦◦◦◦

◦

Figure 13: Predicted Versus Observed RMS Pitch,Time Domain Predictions with Nonlinear Buoy-ancy and Incident Wave Forces

0 5 10 15

Observed Tz Pitch (s)

0

5

10

15

Pre

dic

ted

Tz

Pitch

(s)


..........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................

++

++

+

+

+

•

◦◦

◦

◦

◦

◦

◦ ◦

Figure 14: Predicted Versus Observed Pitch Zero-Crossing Period, Time Domain Predictions withNonlinear Buoyancy and Incident Wave Forces

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DISCUSSION

The Nipigon sea trial included simultaneous mea-surements of ship motions and directional wave spec-tra. Measurements of rudder motions would haveenhanced the value of the data for validation oflateral plane motion predictions. In the absence ofmeasured rudder motions, coursekeeping has beenmodelled using low frequency stiffness terms, andassociated damping terms, for surge, sway and yaw.

The numerical predictions give generallygood agreement with the RMS motions and zero-crossing periods during the Nipigon sea trial. Asexpected, agreement is better for heave and pitchthan for roll. Among the numerical prediction meth-ods, the predicted motions are very similar. Thegood results from strip theory are likely due toNipigon’s slender geometry. Time domain predic-tions using linear and nonlinear forces from buoy-ancy and incident waves give very similar results,likely due to Nipigon having minimal flare near thewaterline at most stations.

The negligible influence of panelled append-ages on the roll radiation damping is likely due tothe small appendage sizes relative to the hull andto the degree of submergence of the appendages.Larger appendages located closer to the free sur-face would have a larger influence on roll radiationdamping. For Nipigon and other ships with smallappendages of large submergence, it appears unnec-essary to include panelled appendages in radiationand diffraction computations.

The scattergrams in Figures 9 to 14 pro-vide further insight into trends. The overpredictionof RMS roll appears to be similar for bow quarter-ing and stern quartering seas. The underpredictionof viscous appendage forces is a possible cause foroverprediction of RMS roll. For RMS pitch, thereis a trend toward overprediction in bow quarteringseas, which could be due to higher amplitude mo-tions. Pitch zero-crossing periods exhibit a trendtoward overprediction in stern quartering seas, pos-sibly due to the assumption of high encounter fre-quency when considering forward speed effects.

Accurate prediction of viscous roll damp-ing forces is still considered to be a major challengefor obtaining accurate ship motion predictions. Thecurrent motion predictions using Kato’s method(1966) for bilge keel roll damping give reasonableroll results. However, the roll motions presented

. . . . . Bare hull

............. ............. ....... Panelled appendages with hull

......................................................... Appendages separate from hull

0 10 20 30

Ship Speed U (knots)

0.00

0.02

0.04

0.06

0.08

0.10

0.12

Roll

Added

Mas

sA

44/I 4

4

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

............. ............. ............. ............. ............. ............. ............. ............. ............. ............. ............. ............. ............. ............. ............. ............. ............. ...........................................................................................................................................................................................................................................................................................................................................................................................................................................

Figure 15: Nipigon Roll Added Mass Versus ShipSpeed at Roll Natural Period of 10.6 s, Zero RollAmplitude

. . . . . Bare hull

............. ............. ....... Panelled appendages with hull

......................................................... Appendages separate from hull

0 10 20 30

Ship Speed U (knots)

0.00

0.02

0.04

0.06

0.08

0.10

0.12

Roll

Dam

pin

gB

44/B

cr

44

. . . . . . . . . . . . . .. . . . . . . . . . . . . .

. . . . . . .

..........................

..........................

..........................

..........................

..........................

..........................

..........................

..........................

..........................

.....................

............................................

.............................................

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.............................................

............................................

.............................................

.........................................

Figure 16: Nipigon Roll Damping Versus ShipSpeed at Roll Natural Period of 10.6 s, Zero RollAmplitude

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from the Nipigon trial are limited to relatively nar-row ranges of RMS values (2.63 to 6.16 degrees) andzero-crossing periods (8.4 to 13.2 s). It is essentialthat roll motions be validated over wide ranges ofmotion amplitudes and frequencies.

CONCLUSIONS

Numerical predictions have been compared withmeasured heave, roll, and pitch for a naval destroyerin multidirectional seas. The numerical predictionsgive generally good agreement with measured RMSmotions and zero-crossing periods. Strip theoryand three-dimensional predictions give very simi-lar results, likely because of the slender hull formof the destroyer HMCS Nipigon. The influence ofappendage radiation forces has been investigatedby including panelled appendages in radiation com-putations. For Nipigon, inclusion of appendages inradiation computations has negligible effect on pre-dicted motions in comparison with the commonlyused approach of treating appendages separatelyfrom the hull and assuming deep submergence. Eval-uation of nonlinear buoyancy and incident waveforces based on the instantaneous wetted hull sur-face has only a minor influence on predicted mo-tions relative to those assuming linear hull forces.

REFERENCES

Ballard, E.J., Hudson, D.A., Price, W.G. and Tem-arel, P., “Time Domain Simulation of SymmetricShip Motions in Waves”, International Journal ofMaritime Engineering, Vol. 143, No. A3, 2003, pp.1–20.

Beck, R.F. and Loken, A.E., “Three–DimensionalEffects in Ship Relative–Motion Problems”, Jour-nal of Ship Research, Vol. 33, 1989, pp. 261–268.

Chakrabarti, S.K., Hydrodynamics of Offshore Struc-tures, Springer-Verlag, 1987.

Himeno, Y., “Prediction of Ship Roll Damping -State of the Art”, Report 239, 1981, Department ofNaval Architecture and Marine Engineering, Uni-versity of Michigan.

Kato, H., “Effects of Bilge Keels on the Roll Damp-ing of Ships”, Memories of the Defence Academy,Japan, Vol. 4, 1966.

Lloyd, A.R.J.M., Seakeeping: Ship Behaviour inRough Weather, Ellis Horwood, Chichester, Eng-land, 1989.

McTaggart, K., “Lateral Ship Motions and Sea Loadsin Waves Including Appendage and Viscous Forces”,International Shipbuilding Progress, Vol. 47, 2001,pp. 141–160.

McTaggart, K., Datta, I., Stirling, A., Gibson, S.,and Glen, I., “Motions and Loads of a HydroelasticFrigate Model in Severe Seas”, Transactions, Soci-ety of Naval Architects and Marine Engineers, Vol.105, 1997.

Meyerhoff, W.K., “Added Mass of Thin Rectan-gular Plates Calculated from Potential Theory”,Journal of Ship Research, Vol. 4, 1970, pp. 100–111.

Papanikolaou, A.D. and Schellin, T.E., “A Three–Dimensional Panel Method for Motions and Loadsof Ships with Forward Speed”, Schiffstechnik (ShipTechnology Research), Vol. 39, 1992, pp. 147–156.

Schellin, T.E., Chen, X.-B., Beiersdorf, C. and Maron,A., “Comparative Frequency Domain SeakeepingAnalysis of a Fast Monohull in Regular Head Waves”,21st International Conference on Offshore Mechan-ics and Arctic Engineering, Oslo, 2002.

Schmitke, R.T., “Ship Sway, Roll, and Yaw Mo-tions in Oblique Seas”, Transactions, Society ofNaval Architects and Marine Engineers, Vol. 86,1978, pp. 26–46.

Wheeler, D.J, “Method for Prediction of ForcesProduced by Irregular Waves”, Journal of Petro-leum Technology, 1970, pp. 359–367.

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validation of ship motion predictions with sea trials data

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