DYNAMIC BEHAVIOUR AND OPERATIONAL LIMITS OF STABILISER FINS

Guilhem Gaillarde*

Maritime Research Institute Netherlands MARIN2, Haagsteeg P.O. Box 28

6700 AA Wageningen, the Netherlands*: Corresponding author’s email: G.Gaillarde@marin.nl

ABSTRACT

The efficiency of stabiliser fins is evaluated most of thetime with a quasi-static, steady approach, the liftingcharacteristics being obtained from wind or cavitation tunneltests. Although this approach can be assumed to be correct whenthe fins are working at low angle of attack in mild seaconditions, strong non-linearity appears when reaching theirlimits in rougher sea conditions, like stall or cavitation.

The lifting characteristics and behaviour of the finsunder a given control algorithm should be addressed in order todetermine accurately their operational limits, both in terms ofmechanical angle saturation and risk of stalling.

Experimental results obtained in the new Seakeepingand Manoeuvring Basin of MARIN for different vessels anddifferent type of fins are presented. Calculations were alsoperformed with a 3D-diffraction theory code and a 2D-striptheory code in order to get more insight in the hydrodynamicmechanism acting on a stabiliser in activity.

NOMENCLATURE

SI units are used throughout this paper. Forces on the fin arealways given in kN. All values from experiments wereextrapolated to full scale values on basis of Froude's law ofsimilitude. The sign convention of some of the followingparameters is given in Figs. 5 and 6.

Afin Area of the fin [m2]

BC Damping gain [deg/(deg/s)]

CC Restoring gain [deg/deg]

Cfintip Chord of the fin tip [m]

Cfinroot Chord of the fin root [m]

CL Lift coefficient [-]

CDPS Drag coefficient for portside fin [-]

CL-sf Lift coeff based on fin mechanical angle [-]

DFinCL Lateral position of the fin w.r.t. [m]

DFinCog Longitudinal position of the fin w.r.t. cog,positive forward [m]

DFinK Vertical position of the fin w.r.t. keel [m]

Drag Drag, positive aft [kN]

FLong-ff Force longitudinal to the fin in fin-fixed co-ordinate system, positive to the trailing edge[kN]

FTrans-ff Force transverse to the fin in fin-fixedcoord. system, positive upward [kN]

FXsf Longitudinal force on the fin in ship-fixedco-ordinate system, positive to stern [kN]

FZsf Vertical force on the fin in ship-fixed co-ordinate system, positive upward [kN]

GM Transverse metacentric height [m]

Lift Lift, positive upward [kN]

rfin Transverse arm between the cog and 1/3rdof the root of the fin [m]

Sfin Span of the fin [m]

Uship Ship speed [m/s]

Vφ Roll angular velocity [deg/s]

Vθ Pitch angular velocity [deg/s]

VZ Heave velocity [m/s]

Z Heave motion [m]

αm Mechanical fin angle in ship-fixed co-ordinate system, positive nose up [deg]

αefin Effective angle of attack of the flow on finin fin-fixed co-ordinate system, positivenose-up [deg]

αflow Effective angle of attack on fin includingorbital velocity of water particle [deg]

fin

LC

δαδ

Lift curve slope [rad-1]

φ Roll angle [deg]

θ Pitch angle [deg]

ρ mass density of sea water = 1.025 t/m3

INTRODUCTION

The efficiency of stabiliser fins is evaluated most of thetime with a static, steady approach, the lifting characteristicsbeing obtained from wind or cavitation tunnel tests. Theperformance of a stabiliser fin in such type of set-up is likely tobe over-estimated, compared to what is measured when the finsare fitted on the hull of a vessel, as shown by Conolly [1969]and Lloyd [1972].

When fitted on a hull, other types of interference mightappear, as lift degradation due to bilge keel-hull interference, seeCox [1977] and Dallinga [1997], or as improvement in the finperformance due to hull-fin interference, see Dallinga [1993].Allan [1945] already noted interference between fins and bilgekeels in 1945 but, surprisingly, this problem still remains insome recent design.

CL

When the effective lift characteristics of the fins aredetermined, taking into account all types of interference, thedamping provided by the stabiliser fins is generally treatedlinearly within any simulation programs, 2D strip theory or 3Ddiffraction theory codes. Although this approach can be assumedto be correct when the fins are working at low angle of attack inmild sea conditions, strong non-linearity appears when reachingtheir limits in rougher sea conditions, like stall or cavitation.

The lifting characteristics and behaviour of the finsunder a given control algorithm should be addressed in order todetermine accurately their operational limits, both in terms ofmechanical angle saturation and risk of stalling. These effectsare known to be of importance in the actual lift and dragprovided by a stabiliser, but they are usually not addressed in thedesign of the fins. One of the reasons is that it is rather difficultto investigate numerically and experimentally and that not manyexperimental data are available.

Results obtained in the new Seakeeping andManoeuvring Basin of MARIN for different vessels anddifferent type of fins are presented and used to investigate thedynamic effects on the lift and drag of stabiliser fins, as well ashysteresis effects and risk of stalling.

Calculations with a 3D-diffraction theory code and a2D-strip theory code were also performed after the tests in orderto get more insight in the hydrodynamic mechanism acting on astabiliser in activity. Since it is possible to measure the forcesacting on a stabiliser fin during tests in model basin, theeffective angle of attack of the flow on the fin, including hullinterference, vessel’s motion and wave orbital velocities can notbe measured easily, necessitating the use of numerical models.

MODEL TESTS TECHNIQUES

Seakeeping and Manoeuvring BasinThe test were performed in the new Seakeeping and

Manoeuvring Basin, which measures 170*40*5 meters in length,width and depth respectively. A main carriage can travel in thelength of the basin up to 6 m/s and a sub carriage, carryingrecording equipment and personnel, can travel in the width ofthe basin up to 4 m/s.

Connections between model and carriage consistedonly of free-hanging wires for relay of measurement signals andpower supply. These cables did not restrict the motions of themodel in any way.

0 10 20 30 40 50

AdjustableBeach

Main Carriage6 m/s

Subcarriage4 m/s

ObservationCarriage

Flap TypeWave Maker

37.5 m

5 m

OffshoreBasin

Seakeeping &Manoeuvring Basin

Figure 1: The Seakeeping and Manoeuvring Basin

The basin is equipped with a total of 331 flap typewave generators, each driven by its own electrical motor. Thisset-up facilitates the generation of long-crested and short-crestedwaves, regular or irregular, from any direction with respect tothe course of the vessel. In the present study, only long-crestedregular and irregular waves were used. The details of the basincapabilities and features were described by Dallinga [1999]. Aview of the basin is shown in Fig. 1.

The focus was of course made on stern-quarteringwave direction, which is the most unfavourable heading in termsof roll for a ship sailing at forward speed. Indeed it is the mostdemanding heading in terms of fin stabiliser efficiency. Testswere performed for other wave directions, from head to beamseas. Some tests were also performed with the model captive inwaves and calm water.

Vessels and fin stabilisersThree different types of vessel were used during

contract research projects in the new Seakeeping andManoeuvring Basin. Each model was self-propelled and kept oncourse by an autopilot reacting on course deviation, rate of turnand lateral displacement. The fins used on the three vessels areoutlined in Figs. 2,3 and 4, together with the shape of the sectionwhere they were located. The characteristics of vessels and finsare outlined in Tables I and II.

• A 180 m high speed Ro-Ro ferry, calm water speed of 35knots, equipped with one pair of high aspect ratio stabiliserfins and no bilge keels. The model was built at a scale of 1to 40.

Figure 2: Stabiliser fins fitted on the 180 m high speed Ro-RoFerry

• A 83 m motor yacht, calm water speed of 16 knots,equipped with two pairs of low aspect ratio (trapezoidal)stabiliser fins and bilge keels. The model was built at ascale of 1 to 16. Only the forward pair of stabiliser fins wasinstrumented.

Figure 3: Stabiliser fins fitted on the 83 m motor yacht

• A 170 m high speed conventional Ro-Ro ferry, calm waterspeed of 26 knots, equipped with high aspect ratio fins withflap and bilge keels. The model was built at a scale of 1 to38.

Figure 4: Stabiliser fins fitted on the 160 m Ro-Ro ferry

Descriptionhigh speedferry

motoryacht

high speedconventionalferry

VesselLpp [m]

Beam [m]Draft [m]GM [m]

Roll period [s]Uship [kn]

180.025.06.52.9

12.2535

83.016.04.21.511.316

170.028.56.53.514.026

Table I: Main particulars of tested vessels

Descriptionhighspeedferry

motoryacht

high speedconventionalferry

FinsArea [m2] 9.9 5.6 7.8

Span [m] 4.4 1.8 3.95

Chord root [m] 2.25 3.54 1.97 **

Chord tip [m] 2.25 2.71 1.97

Aspect ratio* [-] 1.95 0.57 2.0

Thickness tip [m] 0.47 0.22 0.466

Thickness root [m] 0.47 0.57 0.466

Inclination [deg] 47 43 19* : span divided by mean chord** : including flap

Table II: Main particulars of the instrumented fins

Instrumentation and measurementsThe shaft of the fin was instrumented with dedicated

force transducers. This instrumentation allowed themeasurement of the force transverse and longitudinal to the fin,as shown in Fig. 5. The forces were measured in a fin fixed co-ordinate system. In order to know the lift and the drag from thefin, the measured forces had to be projected with respect to thelocal flow direction on the fin. The definitions of the lift anddrag forces as well as the effective angle of attack of the flow onthe fin are shown in the following Fig. 6. The instantaneousangle of attack of the flow on the fin is not measured, thereforesome approximations were made to obtain the instantaneous liftand drag from the measured forces. The approximations andformula used are detailed in the following.

BOWSTERN

FZPS_sf

FTransPS_ff

Ftotal

FXPS_sf

FLongPS_ff

Mechanical fin angle positive nose up

+

+

+

+

Figure 5: Forces measured in fin-fixed co-ordinate system andprojection in ship-fixed co-ordinate system

FTransPS_ff

Ftotal

FLongPS_ff

+

+FLOW

LIFTPSfin

DRAGPSfin +Effectiveangle of attack

Figure 6: Definition of the lift and drag forces and the effectiveangle of attack of the flow on the fin

Model test programThe model test program for each vessel consisted in

verifying different aspects of the behaviour and performance in awide variety of sea state and wave directions. During all thetests, from head to following seas, the forces on the fins and thefin angles were measured. The selected sea state usuallyconsisted of an average and an extreme condition, in order toobserve the behaviour in normal operating condition but also inconditions when non-linearity would occur. For the stabiliserfins, these non-linearities consisted of stalling, fin emergence orlarge flase angle of attack.

Concerning the tests in stern-quartering seas, selectionof the most unfavourable heading concerning roll motion wasbased on a preliminary set of strip theory calculations. Fig. 7illustrates the contour plot of the roll response of the 180 m highspeed ferry, as a function of heading and wave frequency. Fromthis type of plot, not only the heading could be selected, but alsothe wave frequencies to conduct regular wave tests. During thesetests, the basic fin characteristics could be determined in termsof lift slope curve as a function of fin angle and drag to liftrelation. The tests in stern-quartering seas were conducted withactive and passive fins.

Different gains were applied, depending on the finreactions in a given sea state. Starting from "standard" gainvalues, those were decreased when the maximum fin angleswere reached too often or increased if higher fin angle could beused.

The following Eq.(1) shows the fin reaction as afunction of the instantaneous roll angle and roll velocity:

φα φ .. CCm CVB += (1)

with Bc and Cc representing the damping and the restoring gain.Standard values used for these gains were in the order of 10deg/(deg/s) for the damping gain and 0 deg/deg for the restoringgain.

Figure 7: Contour plot of roll response at 35 knots as a functionof heading and wave frequency

During the tests in head and bow-quartering seas, thepenalty in resistance due to the presence of the fins could beestablished. This so-called fin added resistance could also beevaluated for stern-quartering direction, showing that finworking with large angles, in order to provide enough lift, alsocreated a significant resistance for the vessel.

For the 170 m conventional Ro-Ro ferry, tests wereconducted in regular and irregular head seas, both with a freerunning and captive model. The aim of the captive tests was firstof all to obtain the relation between lift and angle of attack byoscillating the fins in calm water, and secondly to obtain the liftand angle of attack due to the incoming and diffracted wave(radiated component being deleted). These tests were importantto check the local flow velocity of each component as calculatedby different theories.

TEST RESULTS

Linear fin characteristicsTests in irregular stern-quartering waves with active

fins were used to determine the lift slope curve and relationbetween lift and drag. Relatively mild wave conditions wereselected, in order to avoid fin angle saturation and possible non-linear effects.

The first example concerns the 35 knots high speedferry, equipped with high aspect ratio fins. The following Fig.8presents the time trace of the fin angle during a half an hour runin 3.0 m significant wave height, 7.0 seconds peak period and 75deg heading. The ship speed was 34 knots during this run. Aremarkable aspect of this time trace is that its nature is ratherregular in appearance, even though this test was performed inirregular wave.

The forces measured in fin-fixed co-ordinate systemwere projected on the ship-fixed co-ordinate system. The newset of forces obtained correspond to a resistance force (positiveto the stern of the vessel) and a vertical force (positive upward).

50 60 70 80 90 100 110 120 130 140 15020

10

0

10

20

time in seconds

φ

Vφ

α finSB

t

.

Figure 8: Time trace of fin angle, roll and roll velocity inirregular stern-quartering wave

Due to the high speed of the vessel and the relatively low waveheight, it can be assumed that the ship motions and the waveorbital velocities play only a minor role in the angle of incidenceof the local flow on the fin. A "ship-fixed" lift coefficient canthen be defined with respect to the mechanical angle of the fin.This coefficient, calculated at every time step, is defined for theportside fin as:

2_

...2

1)(

)(

shipfin

sfsfL

UA

tFZtC

ρ=

(2)

The following Fig.9 shows this lift coefficient based on the finmechanical angle.

most unfavourablecombination of headingand frequencies

15 7.5 0 7.5 151

0.5

0

0.5

1

fin mechanical angle Portside [deg]

Shi

p-fi

xed

lift c

oeff

icie

nt [

-]

15 7.5 0 7.5 151

0.5

0

0.5

1

fin mechanical angle Starboard [deg]

Shi

p-fi

xed

lift c

oeff

icie

nt [

-]

Figure 9: Lift coefficient of portside and starboard fin as afunction of fin mechanical angle of attack

The bold line in Fig.9 comes from a formulationdeveloped during the CRS motion control project, see Dallinga[1996], which is based on the fin geometry characteristics, itslocation on the hull and section characteristics. For this given finfitted on this vessel the formulation gives:

efinefinfin

LnformulatioCRSL

CC απα

δαδ

.180

.02.3._ == (3)

A first remark is that the local flow and lift onwindward and leeward fins are identical as shown by Fig.9.

In that particular case, the disturbance due to shipmotions, the diffracted waves and the orbital velocities (radiated+ incoming wave) are rather small, yielding a rather good agree-ment between the theoretical formulation and the experiments.

Taking into account the ship motions can refine thedetermination of the effective angle of attack of the flow on thefin. When the vessel heave, pitch and roll heavily, the local flowvelocity at the location of the fins will be affected. Thisinfluence can be regarded as the radiated contribution of thelocal flow velocity. The formulation in Eq.(4) shows how tocalculate the angle of attack for the portside and the starboardfin. However, the real angle of attack of the flow on the fin willalso depend on the orbital velocity of the water particle (due toincoming + radiated wave) and on the diffracted wave, thatcould not be evaluated easily so far.

( )π

θφπ

αα 1802

180 ....

tan

−++=

ship

ZFinCogfinfinEfin U

VVDVrA (4)

The forces measured on the fin can be projected on aco-ordinate system as defined by the effective angle of attack. In

the following, we will call lift and drag the projections of themeasured forces on this new system of axis, even if the correctco-ordinate system defining the lift and the drag should bealigned with the real flow on the fin that also takes into accountthe orbital velocity of the wave.

The lift and drag coefficients are then defined in thesame way than in Eq.(2). They are written as a function of timein the following Eqs.(5,6):

2...2

1

)()(

shipfin

L

UA

tLifttC

ρ=

(5)

2...2

1)(

)(

shipfin

D

UA

tDragtC

ρ=

(6)

No much differences are observed when comparing the lift slopecurves from Figs. 9 and 10, illustrating the fact that for this highspeed vessel in low waves, the mechanical angle is already agood approximation of the effective angle of attack.

15 7.5 0 7.5 151

0.5

0

0.5

1

Effective angle of attack [deg]

Lif

t coe

ffic

ient

[-]

.

Figure 10: Lift coefficient of portside fin as a function ofeffective angle of attack

A typical parabola curve describes the relation between the liftand drag, as shown by Fig.11. The relation is given by thefollowing Eq.(6)

20 .LiftcDDrag += (6)

with D0 being the frictional resistance of the fin equal to 42 kNand c equal to 0.0001.

1000 500 0 500 10000

100

200

300

400

Lift [kN]

Dra

g [

kN]

.

Figure 11: Relation between drag and lift on starboard fin

o experimental data points

CRS Motion Control WG formulation

Same type of results was obtained in a low sea statefor the motor yacht and for the high speed conventional ferry,see Fig.12. For the latter, static fin angles were tested at forwardspeed with a captive model in calm water. The results are shownwith circles in Fig.12.

200.8

0.4

0

0.4

0.8

Lif

t coe

ffic

ient

[-]

200.8

0.4

0

0.4

0.8

Lif

t coe

ffic

ient

[-]

Figure 12: Lift coeeffective angle of atta

The experiobtained from a test significant wave heigdiscrepancy in the lifInteraction with the wmight be the reason working in a much Fig.12 top.

Effective angle of attIn the previ

attack is based on theave, pitch and rollvelocity componentsattack of the flow on different approach can

Let us firstcoefficient Cl and thethe relation between found from a test in lare shown in the Eqsassume these relation

as the system remains linear. The total force measured on the finis given in Eq.(7):

22

2_

2_

DragLift

FFF ffTransffLongTfin

+=

+=(7)

o static test with captive model

10 0 10 20

Effective angle of attack [deg]

10 0 10 20

Effective angle of attack [deg]

fficient of portside fin as a function ofck

mental data presented in Fig.12 werein irregular stern-quartering wave of 2.5

ht, at a speed of 25 knots. It shows a cleart between the leeward and windward fin.ave orbital velocities and diffracted wavesfor such discrepancy. The leeward fin ismore sheltered environment as shown in

ack calculated from the total forceous section, the so-called effective angle ofhe ship speed, fin mechanical angle and induced velocities (so-called ship motion). In order to evaluate the true angle ofthe fin, including all velocity component, a be taken.

assume that the relation between the lift angle of attack αFin is known, as well asthe lift and drag forces. These relations,

ow stern-quartering waves with active fins,.(3, 6) for the 180 m high speed ferry. Wes to be valid in any circumstances, as soon

Combining Eqs (3, 5, 6, 7) provides a second orderequation as given in Eq.(8).

2

2

2

20

2

2

2

222

.....2

1.

.....21

++

=

+=

flowfin

Lshipfin

flowfin

Lshipfin

Tfin

CUAcD

CUA

DragLiftF

αδαδρ

αδαδρ

(8)

By solving this equation at every time step, one canobtain the effective angle of attack of the flow on the fin,including the wave orbital velocity. Fig.13 shows thecomparison of the time domain signal of the effective angle ofattack on the fin calculated on one hand from the ship speed, finmechanical angle and ship motion’s velocities and on the otherhand from the total measured force and the ideal lift-dragcharacteristics of the fin. It shows for this low sea state arelatively similar angle of attack, except in the maximumnegative amplitude (fin nose down) which is slightly higherwhen calculated from the measured total force. Concluding thatthis difference is due to the diffracted and radiated componentsis a bit too fast in view of the stage of this research. Furtherwork, both experimental and numerical, will be needed to fullyunderstand that point.

Fig.14 shows the same data for the leeward fin. Thetwo signals are a bit closer than for the windward fin in Fig.13.

0 5 10 15 20 25 3020

0

20

40

time [s]

angl

e of

atta

ck [

deg]

.

Figure 13: Angle of attack on windward fin calculated in twodifferent ways

0 5 10 15 20 25 3020

0

20

time [s]

angl

e of

atta

ck [

deg]

.

Figure 14: Angle of attack on leeward fin calculated in twodifferent ways

leeward fin

windward finangle of attack based on ship speed +fin mechanical angle + ship motions’sinduced velocities angle of attack based on total

measured forces + fin lift-draglinear characteristics

Non-linear fin characteristicsThe same tests than those presented in the previous

sections were performed in higher significant wave height. Non-linear behaviour of lift started to appear. Fig.15 presents the timetrace of the lift in a 5.5 m significant wave height, stern-quartering direction and 34 knots. The fin stabiliser clearlyexperiences stall in such wave conditions. The resulting rollangles measured were in the order of +/- 20 degrees.

450 475 500

1000

0

1000

2000

time [s]

|ift [

kN]

.

Figure 15: Stall measured on high aspect ratio fin

The resulting lift-angle curve presents a differentcharacteristic than previously: typical drop in lift at an angle ofattack around 25 degrees is shown in Fig.16. In that particularcase, the stabiliser fin was reaching its maximum mechanicalangle at the time stall occurred. Fig.16 also shows a hysteresisloop. When the dynamic change of angle of attack reverses theflow on the fin, the lift does not revert to the value encounteredat the lower angles, but fall below these values (even to negativevalues). Hoerner [1985] described this hysteresis effect.

50 25 0 25 501.5

0.75

0

0.75

1.5

Effective angle of attack [deg]

Lif

t coe

ffic

ient

[-]

.

Figure 16: Lift as a function of angle of attack and hysteresiseffect due to stall

Fig.17 shows a typical relation between lift and dragduring stall. This figure shows the dramatic increase of dragwhen the fin is stalling but it also shows negative drag values.

In the present situation, the tested significant waveheight was clearly too high for the fin stabiliser system, the finsalways reaching their maximum mechanical angle even withvery low gain. There is no evidence in the present case that stalloccurred because the fin reached its maximum mechanical angleof attack. Further work need to be undertaken in that area.

2000 1500 1000 500 0 500 1000 1500500

0

500

1000

1500

2000

2500

Lift [kN]

Dra

g [

kN]

.

Figure 17: Lift and drag

A much more interesting case was observed in a lowersea state. In a 30 minutes equivalent full time test, in 3.0msignificant stern-quartering wave, stall occurred only once in agroup of higher waves. This relatively rare event is first of alldue to the fact that for this type of heading the encounterfrequency is low and secondly because the fins “need” a giventhreshold wave height to start stalling. In the case presented inFig.18 the lift degradation is such that during several seconds thevessel behaves as if no fin was present on the vessel. After thisgroup of high waves, lift characteristics became again linear andresulting roll angles decreased dramatically.

There is clearly a threshold condition where fins reachtheir limits and become ineffective. The problem remains indefining if this limiting condition is acceptable or not for themission of the ship.

0 200 400 600 800 1000 1200 14004

2

0

2

4

6

8

time [s]

Rol

l ang

le [

deg] .

Figure 18: Time trace of roll in stern-quartering irregular seasand sudden roll angle due to stall in a high group of waves

This type of tests highlights the fact that the testduration, especially at low encounter frequency, must be longenough to be sure to encounter non-linear effects or events withlow probability of occurrence.

An attempt to obtain a trend for the maximumoperational conditions has been made by subdividing the test inseveral tests of shorter duration. The graph presented in Fig. 19was obtained by calculating the standard deviation of roll andthe significant wave height of each sub-test. Of course this resultis very sensitive to the specified duration of the sub-tests but theresult looks relatively realistic.

linear behaviour of lift and roll

linear behaviourof lift and roll

non-linear behaviour of lift and roll,stall of fin stabilisers

0 1 2 3 4 5 60

1

2

rmsroll

Hssubtest

Figure 19: Non-linear roll behaviour

Such behaviour of the stabilising system can not beinvestigated through classical linear approach in frequencydomain. The non-linear relation between lift coefficient andangle of attack should be included in further numerical work inorder to obtain the correct ship motions under thesecircumstances and a time domain approach should be used.

Added resistance due to finsWhen projected in a ship-fixed co-ordinate system,

both lift and drag produce resistance or thrust for the vessel, asshown in Fig.5.

Fin dimensions tend to be reduced in order tominimise their resistance (drag) in water. However, small finsneed to work at higher angles of attack than larger fins, in orderto produce the same moment. With large requested mechanicalangles, the projection of the lift in ship-fixed co-ordinate systemyield large added resistance. The following example shows inFig.20 the time trace of the added resistance of the forward pairof stabiliser fins on the motor yacht. Two different gains andpassive fins were used during the tests, resulting of course indifferent roll behaviour but also in a different mean addedresistance. Results are given in Table III for tests in stern-quartering seas.

0 300 600

0

100

time [s]

Add

ed r

esis

tanc

e [

kN]

.

Figure 20: Added resistance due to fin in stern-quartering seas,Beaufort 6 wave condition and 16 knots

gain appliedrms roll

[deg]

mean addedresistance

[kN]Beaufort 6 - Hs=2.9 m

fin passive 5.9 3.1

Bc = 10 deg/(deg/s) 1.9 14.8

Bc = 20 deg/(deg/s) 1.2 15.6

Beaufort 4 - Hs=1.7 m

fin passive 2.9 3.6

Bc = 10 deg/(deg/s) 1.0 7

Bc = 20 deg/(deg/s) 0.6 8.3

Table III: Standard deviation of roll and added resistance forthree different control settings in stern-quartering seas, 16 knots

Low aspect ratio trapezoidal fins can not be retracted,yielding usually added resistance in water. Typically they arebelieved to "cost" resistance for the ship for headings where theyare not useful to damp the roll. The following table summarisesthe resistance penalty generated by the forward fins of the motoryacht in different sea states. A surprising result shown in TableIV is that, due to the false angle of attack generated by the waveorbital velocities and ship motions, the penalty in the highestwaves is almost zero.

gain appliedBc = 10 deg/(deg/s)

mean addedresistance

[kN]

BF4 - Hs=1.7 m - Hship = 16 kn 2.5

BF6 - Hs=2.9 m - Hship = 14 kn -0.7

BF8 - Hs=3.5 m - Hship = 8 kn 0.2

Table IV: Mean added resistance in head seas

CALCULATIONS

A research study undertaken by Naaijen [2000]showed that good agreement between calculations and modeltests was obtained. The calculations were performed with twoin-house developed program, PRECAL and S2D. Both programsare based on linear theory. The first one is a three-dimensionaldiffraction program and the second one is a two-dimensionalstrip theory program that includes diffraction.

Calculations were repeated for the vessels used in thepresent study. Fig.21 illustrates the good agreement with the 3Ddiffraction theory program PRECAL on the effective angle ofattack obtained on the leeward fin of the motor yacht, in stern-quartering regular waves. The agreement was relatively poor forthe windward fin, as shown in Fig.22.

20 30 40 50 60 70 80 90 100

2

0

2

time [s]

Eff

ectiv

e an

gle

of a

ttack

[de

g]

.

Figure 21: Comparison between measured and calculated(PRECAL) effective angle of attack on leeward fin in regularstern-quartering wave, µ = 60 deg - ω = 0.9 rad/s - 16 knots

20 30 40 50 60 70 80 90 100

2

0

2

time [s]

Eff

ectiv

e an

gle

of a

ttack

[de

g]

.

Figure 22: Comparison between measured and calculated(PRECAL) effective angle of attack on windward fin in regularstern-quartering wave, µ = 60 deg - ω = 0.9 rad/s - 16 knots

[deg]

[m]

The same results were obtained with the 2D striptheory code, as shown in Figs.23 and 24.

20 30 40 50 60 70 80 90 100

2

0

2

time [s]

Eff

ectiv

e an

gle

of a

ttack

[de

g]

.

Figure 23: Comparison between measured and calculated (S2D)effective angle of attack on leeward fin in regular stern-quartering wave, µ = 60 deg - ω = 0.9 rad/s - 16 knots

20 30 40 50 60 70 80 90 100

2

0

2

time [s]

Eff

ectiv

e an

gle

of a

ttack

[de

g]

.

Figure 24: Comparison between measured and calculated (S2D)effective angle of attack on windward fin in regular stern-quartering wave, µ = 60 deg - ω = 0.9 rad/s - 16 knots

CONCLUSIONS

Based on the present set of model tests andmeasurements of fin lift and drag forces on three differentvessels, the following conclusions can be made:

• In low sea state, prediction of fin performance is welldescribed in linear terms. The lift remains proportional tothe local angle of attack of the flow on the fin.

• For a high speed vessel with fins located around midship, inlow sea state, the mechanical fin angle is a goodapproximation of the effective angle of attack of the flow.At lower speed the ship motions and the incident wavecontribute significantly to the effective angle of attack

• There is an angle of attack when non-linearity appears inthe lift characteristics, yielding stall. This lift degradationyields also non-linearity in the roll behaviour in wavesexceeding a particular threshold height.

• The resulting behaviour of the vessel when fins are stallingcan not be predicted with classical linear theory approach.However, as local flow velocities and effective angle ofattack can be calculated reasonably well, a time domainapproach with a non-linear fin reaction on local angle ofattack might be a solution to investigate further thebehaviour of the vessel.

• Further work is needed to evaluate the behaviour of the finsunder large angles of attack and high speed, including stalland cavitation.

• A good sizing of the stabiliser fins is important to minimisethe requested angle of attack. Low angles of attack inworking conditions will reduce the risk of stalling, will

minimise the added resistance in waves and will increasethe limiting wave condition in which maximum mechanicalangle will be reached. The design target for stabilisers maybe a limiting wave condition in which the mechanical limits(fin angle, velocity) and hydrodynamic limits (stall,cavitation) are reached simultaneously.

• The mean added resistance due to fins in head seas can bevery low and even negative, providing a mean positivethrust.

REFERENCES

Allan J.F., The Stabilisation of Ships by Activated Fins, Trans.RINA, Vol.87, 1945.

Conolly J.E., Rolling and its Stabilisation by Active Fins, Trans.RINA, Vol.111, No.1, January 1969.

Cox G.G., Lloyd A.R.J.M., Hydrodynamic Design Basis forNavy Ship Roll Motion Stabilisation, SNAME Transactions,Vol.85, pp.51-93, 1977.

Dallinga R.P., Hydromechanic Aspects of the Design of FinStabilisers, RINA Spring Meetings, 1993.

Dallinga R.P., Doeveren A.G., Co-operative Research Ships -Motion Control Task 6 Validation Tests, MARIN reportNo.411105-2-ZT, Maritime Research Institute Netherlands,1996.

Dallinga R.P., van Wieringen H.M., Passenger comfort onboard Motor Yacht, , HISWA, th eNetherlands, 1997.

Dallinga R.P., The New Seakeeping and Manoeuvring Basin ofMARIN, , Int. Workshop on Natural Disaster by Storm Wavesand their Reproduction in Experimental Basin, Kyoto, Japan,1999.

Naaijen P., Local Water Velocities, MARIN report No.16129-2-CPS, Maritime Research Institute Netherlands, 2000.

Hoerner S.F., Borst H.V., Fluid-Dynamic Lift, Hoerner FluidDynamics, 1985.

Lloyd, A.R.J.M., Roll Stabiliser Fins: A Design Procedure,Trans. RINA, 1974.