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Maritime Research Institute Netherlands

Lab.

v.

Scheepsbouwkunde

Technische Hogeschool

Delfi

2, Haagsteeg, P.O. Bx 28

6700 M Wageningen, The Netherlands

Telephone ± 31 8370 93911 Telex 45148 nsmb ni Telefax+ 31 8370 93245

Z 50831 - Publication ONR

1988

DEVELOPMENT OF DESIGN TOOLS

FOR THE PREDICTiON OF SWATH

MOTIONS

R.P. Dallinga

Ross Graham

R.H.:M. Huijsmans

(2)

ABSTRACT

A seakeeping research pmam to develop a physical

understanding Of SWATH motions and improved prediction methods is described. It is found that hull-fin interactions arid free-surface effects are sign cant and difficitto quantify by ixnple means. The merits of a

simplifi4 method combining three-dimensional diffraction theOry with empirical infOrmation on the loads are evaluated, as well as those of a strip-theory method, Although reasonable correlation for pitch and heave in head and bOw seas is obtained using the simpli&d method, it is concluded that accurate predictions of the behaviour of a SWATH in waves will require a more detailed description of the dynamics of the flow around the vessel.

NOMENCLAT.RE

A finazea

effective aspectratlo

Aw wetted area of the SWATH heave d*iiping coefficient C average chord of the fm

lift curve slope

(Ci.)w

lift curve slope of the wing alone

(CInJW)

lift curve slope of the body induced by the

vng

(CLa)w(B) lift curve slope of the wing in the presence of the body

Cp non-dimensional pressure coefficient,

Cp P/(O.5pV)

non-dimensional force coefficient,

C= F2I(O.5pV Aw)

FX longitudinal force FY lateral force

FL vertical force

FL H vertical force on the hulls

KB (Cl..&B(W) I (CLnJw

Kw)

lift amplitude

MY H pitch moment on the hulls

n unit vector

P presswe

r

radius of the hull where the fin is attached distance from the hull axis to the tip of the fin

V ship speed

Development of Design Tools for the Prediction of SWATH Motions

R.P. Dallmga', Ross Grahamt, and R.H.M. Huijsinans°

* M ithifle Research Institute of the Netherlands, Wageningen

tDefence Research Establishment Atlantic, Daroruth, Nova Scotia, Canada

heave amplitu4e

amplitude of the vertical component ofthe wave orbital velocity

aa

arnp]itude of the angle of attack Wave amplitude

vertical elevation of the freesurface

p density of water

cI potential

$3 roll amplitude

potential describing stationary component of the flow

I. INTRODUCI'ION

This paper describeS some of the results of a seakeeping research proam carried out as part of the Canada/Netherlands SWATHproject. This project was jOintly sponsored by Defence Research Establishment Atlantic (PREA) and the Royal Nçtherlands Navy. The goals of the research included providing systematic seakeeping resistance and propulsion model data and developing improved theoretical methods for predicting SWATH performance. The thodel tests were conducted at the Maritime Research Institute of the Netherlands

(MARIN), while the analytical work wasperformedbothat MARIN and at DREA. The resistance and propt4sion results are described in Reference 1.

The research on SWATH seakeeping was initially directed towards developing a physical understanding of SWATH modons, with the subsequent goal of developing improved prediction methods Free running and captive model ttsts were conducted in head, quartering, and following seas, and in calm water. The rCsults Of these

tests provided considerable insight into the SWATH motion prob]em and were also useful for evaluating prediction methods. Two computer programs were available at the

start of the study. consistingofathree-diniensional.

diffraction program and a sthp-theory program. A simple method for computing the excitation forces on and motions of a SWATH was developed and evaluated as part of the project This method combines three-dimensional diffraction theory with empirical information on the fin loads.

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As is usual in listearseakeeping theory, the hydrcelynamic problem is dealt with by dividing it into parts. The various components of the hydrodynainic forces on the various elements are aeatedseparately, and

intrference effects are regarded as interactions. A more rational approach would be desirable; however, no maxhexntiral thodel is currently available to describe the

hydrodynamic phenomena in the vcnty of the hulls. The

geornettical elements discerned in the study are the hulls, the stabilizing fins, the rudders, and the propellers. The forces are separated into inertia, drag, and lift components. 2. AVAILABLE MATHEMA11CAL TOOLS

2.1 Hydrodynamic Forces Acting on the Hulls

The wave-induced forces and the motion-induced, reaction forces can be predicted by two- and three-dimensional potential theory methods.

The three-dimensional diffraction program used in our study is based on a boundary integral approach using

source disttibutions over the mean position of the wetted hull of the ship. The Green's functions involved satisfy the linearized free-surface condition, the radiation condition, Laplace's equation, and a condition on the sea floor. The source sttengths are determined from a Fredholme integral equation of the second kind, satisfying the boundary conditions on the mean wetted hull. The zero-speed results of the diffraction program are adapted to account for the effects of forward speed in a simplified manner. It is assumed that the hydrodynarnic reactiOn forces of the vessel at forward speed equal the zero-speed reactiOn forces at the frequency of wave encounter. The wave-induced excitation is determined at the corresponding wave frequency, which is basically a Froude-Ktilov hypothesis. The resulting motions axe obtained by solving the equations of motion at the encounter frequency. Results of this simplified approach have been reported by Huijsthans and Dalhinga (2). Some results based on the exact solution of the fOrward speed problem were reported by Inglis (3).

The two-dimensional Fovam used in the study is the computer program SWATM2 which is described in Reference 4. SWAT is essentially a marriage of the two David Taylor Research Center programs M0T35 arid M0T246 (5) with the added capability of irregular Seas calculations. The programs are based on the theoretical model of SWATH motions developed by Lee (6). This model combines equations of motion and snip theory similar to that described by Salvcsen, Tuck, and Faltinsen (7) with empirical hydrodynanzc coefficients which account for viscous damping and the presence of passive stabilizing

fins.

2.2 Forces Acting on the Fins

The lift anddrag of the control surfaces can be estimated from theoretical and empirical formulae which are given in the literature. The latter are mostly based on wind tunnel data on two-dimensional wing sections. Generally speaking these forces have to be corrected for the finite span of the fins, hull-fin interactions, fin-fin interactions if the fins operate in each other's wakes, and the presence of the free siflfacc. Also, the amplitude of the lift and drag forces may be sensitive to dynamic effects. For a

description of the various methods proposed in the past, the reader is referred to the work of van Walree (8), Whicker and Fehlner (9), McCreight (10), and Hooft (11).

2

A theoretical method of establishing the forces acting on the fins which accounts for both hull-fm and fm-fin interactions and the diffraction of the incident and radiated

wave patterns at forward speed does not exist; however, in calm water, progress can be made. The total (calm-water) potential (x)is written as

(x) = -V5 x + 4,(x)

where $S describes the stationary component of the fluid flow. The stationary component can be evaluated using the approach of Dawsoñ (12). The theoretical principles of Reference 12 were used at MARIN to develop a computer program to calculate the effects of lifting surfaces on the wave resistan e of ships. In the present work, this code is used to establish the diSturbed velocity field near the aft fins of a SWATH vessel. The effect of the free surface is taken mto account in the calculation of the angle of attack of the flow on the fins. Fin-fin interactions are also accounted

for.

The Dawsor method can be described as a boundary integral method with Rankine sources using a linearization about the zero Froude number flow, in Which the free

surface is represented by a symmetry plane. The radiation condition is satisfied using a backward.fthite difference

scheme. The governing equations for are

V =0 in the fluid

(V.n ) S = 0 on the wetted surface of the ship

gii +-(()2 +

()2 + ()2 - V) 0

at the free surface

1ix + - 0 at the free surface

¶75=V5 azinfinity

Waves only propagate dosueam.

The zero speed problem is solved using the methods of Hess and Smith (13). The free surface z=Tl is part of the solution to the problem, and so an iterative scheme is used to determine the wave elevation due to the disturbance of the ship. A fUll description of the development of MAR1Ns Dawson program is given by Raven (14) at this conference.

3. RESULTS OF EXPERIMENTAL AND THEORETICAL WORK

3.1 Description of Experiments

Model

The general arrangement of the SWATH is illustrated in Figure 1, and the main characteristics are given in Table

1. The 1 to 24.1 scale model was constructed of PVC-and wood. The PVC struts arid hulls ensured a strong, durable, watertight construction. The bUlbs along the contoured hulls and the triangular transition between the hulls and

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deck ("fillets") were constructed of wood. The model was fined with one passive central fin connecting the two hulls about halfway along the length of the vessel, and two active fins at the aft part of the hulls.

Table 1: Main Charactistics of SWATH Vessel

The rests were performed in the Seakeeping

Laboratory of MARiN. The test basin measures 100 m by 24 m by 2.5 in. Personnel and recording equipment are carried on a towing carriage, which can travel the length of the basin at speeds up to 4.5 in/s.

The mode] was propelled using inward-turning stock propellers. During the free-running tests, the only

connection between the model and the carriage consisted of free-hanging electric cables for relaying the measurements and the power supply. During the captive tests, the model was fixed below the carnage by means of a six-component force transducer, and the propellers operated at the model cairn-waxer seif-propulsion point. In addition to the overall excitation, the forces on the fins and rudders and the propeller thrust were also measured.

3.2 Forces Acting on the Hull

Wave-Induced Forces

In addition to that provided by the.experiments, some insight into the nature of the excitation.forces was obtained by calculating the diffraction and Froude-Krilov

components separately. Figures 2 and 3 show some of the results. The alculations indicate that the forces in the horizontal plane (sway, roll, and yaw) are dominated by diffraction effects. The surge forces consist mainly of the Froude-Krilov contribution. The heave and pitch forces are a complicated mix of both the Froüde-Krilov and diffraction components, with the relative magnitude of the two force components showing a strong frequency dependence.

In order to study hull interference effects, the calculations performed for the twin hull configuration were repeated for a single hull. Figures 4 and 5 show typical results comparing the excitation force on two hulls with the sum of the results obtained for the individual hulls. The results show that the interference effects are negligible in the surge, heave, and pitch modes, but very strong in the sway, roll, and yaw modes. Interaction effects axe strongest at wave frequencies corrçsponding to

wavelengths on the order of twice the distance between the hulls.

The wave-induced forces measured during the captive tests may be used to get a first appreciation of the lift and drag contributions to the hull excitation. This is

accomplished by subtracting the fin and rudder forces and the propeller thrust from the total force. Of course, the fin-hull interactions will significantly influence the forces on the hull, especially those in the vertical direction. Figures 6 to 9 show some typical.results.

One remarkable result of the investigation is the very good correlation of the theoretical and experimental surge excitation, as illustrated in Figure 6. The relatively small speed dependence suggests that drag and lift effects are small.

The horizontal forces show a strong speed dcpendece and correlate poorly with potential theory results (Figure 7). The frequency at which the

discrepancies are largest suggests that the discrepancy is due to the interactions between the hulls. It seems that interaction effects are magnified by forward speed.

As illustrated in Figure 8, the heave force in head seas shows reasonable correlation between theory and

exper meet at all three speeds tested. On the other hand, the pitch force is systematically overestimated.

In following waves, the heave and pitch excitations show a distinct speed dependency, as illustrated for pitch in Figure 9. Both excitations decrease strongly with.increasing forward speed in high frequency waves; the pitch excitation shows the opposite trend in lowfrequency waves. The speed dependence of the excitation forces at high frequency was originally attributed to the interference of the waves with the propeller wake; however, additional tests with the propellers removed produced alftiost identical.results.

The above observations show that potentiai theory does not immediately yield accurate estimates of the wave-induced forces on the hulls.

Hvdmdvnarnic Reaction Forces

As in the case ofthe wave-induced excitation, a first impression of the reaction forces can be obtained from theoretical calculations using three-dimensional potential theory. The results indicate that the heave and pitch reaction forces are dominated by inertia effecrs the wave-making damping component is very small. In the horizontal plane, both inertia and wave-making effects are

important.

The twin hull calculations were repeated for a single hull to study hull interference effects. The results are similar to those obtained for the wave-induced forces: interference effects are negligible for the surge, heave and pitch modes, but very strong in the sway, roll, and yaw modes. Interaction effects are Strongest at oscillation frequencies related to wavelengths on the order of twice the distance between the hulls.

(Figure 9a)

3.3 Forces on the Fins

Wave-Induced Forces

A first appreciation of the wave-induced forces on the fins can be obtained by assuming that the hulls do not disturb the wave orbital velocities. Under thisassumption, the liftamplitude, La, can be estimated by

2

La= 0.5pAV5 Cj (Za

with a3= ±/V5

where C is the lift curve slope, pis the water density, VS is the ship speed, A is the fin area, aa is the amplitude of

the angle of attack, and ±a is the amplitude of the vertical

Length Between Perpendiculars (in). 108.54

Length of Struts (in) 82.49

Breadth at Cenue Line of Struts (in) 24.38 Depth to Underside of Deck (in) 14.65

Draft (m) 9.01

Displacement (tonnes) 5246.

Design Speed (knots) 30.

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component of the orbital velocity. Based on this approach,

the parameter L /( V5) should be more or less constant for a given fin during the various tests. Measured and

theoretical values of this parameter for the cenmal and starboardaftflnsareshownin Figures lOand 11,

respectively.

As in Reference 6, the lift curve slope of the aft fin in the presence of the hull, (Cl.o)ws). is expressed as

(CL4Z)w(B) = KW) (CJw (1)

where (C)w is the lift curve slope for the fin alone, and Kw is defined by the ratio of the two lift curve slopes in

Equation (1). An expression for KW(B) based on slender body potential theory due to Puts, Nielsen, and Kaatari (15)

is given in Section 3.4. The lift curve slope (Cj)w is

calculated using the empirical expression derived by Whicker and Fehlner (9) for low aspect ratio wings of zero iweep angle:

(CJw

1.8,rA per radian

1.8 + ,j A+ 4

where A is the effective aspect ratio

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ristheradiusofthehullwherethefiflisatlaChed,ro isthe

distance from the hull axis to the tip of the fin, and C is the average chord of the fin. The num rator of Equation (2) is the distance between the tip of the fin and its image in the circle of radius r.

The theoretical predictions for the parameter Lf(±aVs) shown in Figures 10 and II are too lOw, particularly for the aft fins; moreover, the experimental results axe far from constant, This suggests that the local fluctuations in the

angles of attack ax maified by the presence of the hulls.

Some insight into the effects of the hulls on the local angles of attack can be Obtained from diffraction theory. The local disuibution of the vertical velbcitict over the span of the foils can be evaluated from the kno incident and diffraction potentials. Neglecting the effects of forward speed on these velocities, the resulting angles of attack can

be calculated. Representative results of'this exercise are shown itt Figures 12 and 13. They indicate that diffraction effects have a large iznpacton the magnitude of the local angles of anack.however, the magnitude ofthe theoretical results is considerably smll than that observed in the tests. This indicates that the diffraction problem is seong1y

affected by the relatively large forward speed under consideration.

iydrodynamic Reaction Forces

The SWATH motions inaoduce angles of attack on the fins which produce reaction forces. These reaction forces can be regarded as the sum of "restoring",

udamping, and "added mass" components. In the present work, it was assumed that the damping component is due

only to the fluctuating Lift.forces.

As for the wave-induced excitation on the fins, the effrs of the hulls on the local angles of attack will initially be assumed to be small in order to gain some, insight on the fin reaction forces. Under this assumption, the damping is linear and directly proportional to the forward speed, while the restoring component.increases as the square of the forward speed.

The magnitude of the fin and.hull connibutions to the reaction forces were compared. Figure 14 shows sample results for heave damping. It was found that the present.fin configuration is very effective in increasing the'damping forces in heave, and somewhat less effective in the pitch mode. This fin configitrarion also increases the static pitch-heave coupling considerably; moreover, since the fins only react to the pitch angle, this coupling becomes stiongly asyminethc.

3.4 Hull-Fin InteractiOns

The pressure field around a lifting fOil and the pressure field around. the body to which it is attached influence each other. An estimate of the magnitude of these interactions can be Obtained from slender body theory. The total lift curve slope, is expressed as

CLci = (KW(B) + KB(W)) (CLa)W

where

KB(W) = (Cjw) I (Cjw

and (CL(J)B(W) is the lift curve slope of the body induced by'the wing. Pius et al. (15)give the following

expressions for Kw(B) and KB(W).

KB(w.= (I_8)2

((l+5(a

8)+]

_82 [(-8)+2arctan 8])

KB(W) (l_3)2 ((1,42)2

_234

x

[arctan.(g 8)+]

42((i_6)+2am51))

where 8= r/r0.

The magnitude of these terms for the present fin

alTangement axe given in Tablc 2.

Table 2: Hull-Fin Interactions from Slender Body Potential Theory

Aft Fins Centre Fin

KW(B) 1.24 0.41 1.1 1. 0.18

KB/KW(B)

0.33 0.16 0.25 0.14 KW(B) +'

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Its concluded that hull-fin interactions significantly increase the effectiveness of the fins, and that the conoibutiOn ofthehulls to the total liftis important, particulaEiy for the aftflns.

In calm water, further insight into the interaction problem can be obtained from the Dawson program

(12),(14). The vertical force, FZ, on the SWATH and on

various subsections of it was calculated for a speed of 20 knots. Table 3 presents the results in terms of the non-dimensional coefficient C defined as

C= FZ/( 0.5pV

where Aw is the wetted area of the vessel.

Table 3:. Hull-Fin Interactions from General Potential Theory

Ca C2

with free-surface effects no free-surface effects

The C2 values shown are for the whole SWATH. Table 3 shows that the effects of the aft fins on the vertical force on the hulls is significant. The influence of the aft fins on the pressure distribution is shown jn Figures 15 and 16 which show lines of constant pressure. Adjacent contour lines have

=0.0025 where Cp = P/(0.5pV), and P is

pressure.

The influence of the fr stefce is also investigated in Table 3 It is concluded from these results that free surface effects are not negligible.

The velocity distribution at the centre line of the aft fin was calculated with no aft fin present. These results were used to calculate the angles of attack at the positions shown in Figure 17. The results are shown in Table 4.

Table 4: Angles of Attack at the Aft Fin Position I Position 2 PoSition 3

Angle of Attack 2.0 2.2 3.3

(degrees)

Using the angle ofattack at Position 2 to calculate the vertical force on the aft fin leads to a value of 3.14 for

(CVs).

The approach of Section 3.3 leads to (CJ)W) = 3.39 for

this configuration.

3.5 Motion Response

Simplified Frequency Domain Model

For design purposes, it would be desirable to develop a si.mplefrequency domain model for predicting SWATH

motions. The fins provide the dominant contiibution to the vertical daxnpingforces at moderate to high forward speed. These forces are linear, which suggests that the

development of such mode1s is wOtth pursuing. A simplified model was investigated, based on the following assumptions:

The hydrodynamic reaction forces acting on the hulls are speed- independent and can be evaluated by potential theory.

The wave-induced excitation is speed-independent and can be approximated by potential theory

excitation and reaction forces acting on the fins can be evaluated by neglecting the influence of the hulls on the local angles of attack. The fin-hull interactions may be accounted forby a frequency-independent magnification factor.

Calculations were mide using this model

incorporating three-dimensional diffraction theory results, empirical information on the fin loads, and a magnification factor of two Representative results are shown in Figures

18, l9and2Oforaforward speed of 12.5 knots. It is is

concluded that this simple approach gives a very reasonable prediction of the pitch and heave responses in head to beam seas. The heave response is also reasonably well predicted in following seas, but the pitch prediction is poor. The accuracy of the predictions of the horizontal motions is disappointing.

Strip Theor

Motion predictions were made using the sthp theory program SWATM2 (4) described earlier. Sample results are included inFigures 18-20. The heave predictions were

good at all headings to the sea, but the pitch predictions were fair at best The predictions of the motions in the horizontal plane were poor.

CONCLUDING REMARKS

The results of potential theory calculations on the hydrodynamic characteristics of the hull indicated large differences in the nature of the forces in the vica1 and horizontal planes. In the vertical plane, the wave-induced excitation forces in heave and pitch were a complicated mi.trure of Froude.Krylov and diffraction effects, while the surge excitation was dominated by the Froude-Krylov component The reaction forces were dominated by inertia effects, with negligible wave-making damping In the horizontal plane the wave induced excitation was domnated by diffraction effects. The reaction forces consisted of added mass and damping contributions of comparable magnitude.

The potential theoty results also showed that hull interference effects are negligible in surge, heave, and pitch, but large in sway, roll, and yaw. The interactions are largest at frequencies corresponding to wavelengths of twice the hull separation.

A comparison of the measured and predicted excitation forces showed that potential theory predictions are of limited accuracy. The discrepancies are largest in the horizontal plane.

It was found that the fins contribute strongly to both the wave-induced excitation forces and the hydrodynamic

aftfins

noaftfins

aftflns

noafifins

Aft Fins 0.00122 - 0.00086

-Hull -0.00296 -0.00356 -0.00148 0.00184

Cerure Fin 0.00186 0.00190 0.00036 0.00038 Total

0.00012 -0.00166

-0.00026 -0.00146

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reaction fortes. Predicting the maiitude of the waver induced forces tVa.s found to be difficult, because the hulls disturb the orbital motions in the incident wave.

It was concluded from the results of slender body theory that the effectiveness of the fins is enhanced by the hull-fin interactions, and that the hull conthbution to the forces introduced by the hull-fin system is important.

The influence of the free surface onthe fins was studied in calm water, and found to be important.

From the above discussion of the nature of the forces, it is concluded that aceurate predictions of the behaviour of a SWATH in.waves will require a detailed description of the dynamics of the flow around the vessel. This is especially mie for the horizontal plane in Which interaction effects are largest.

Measured motions were compared with the

predictions of a simplified method which combined three-dimensional diffraction theory with empincal information on the fln loads. Reasonable coirelation was obtained for the heave response at all headings, and the pitch response in head and beam seas. The coitelation shown by the sway, roll, and yaw responses was disappointing.

The merits of a strip theory program were also investigated. Theheave predictions were good. but the pitch predictions were fairat best. The predictions ofthe motions in the horizontal plane were poor.

ACKNOWLEDGEMENT

The research was jointly sponsored by Defence Research Establishment Atlantic and the Royal Netherlands Navy. Permission to publish is gratefully acknowledged. REFERENCES

Koops, A. and Nethercote, W.C.E.: "SWATH Model Resistance Experiments", mt. Conf on SWATH Ships and Advanced Multi-Hulled Vessels, RINA, London, April

1985w

Huijsrnans, R.H.M. and Dallinga, R.P.: "Non-Linear Ship Motions in Shallow Water", International Workshop on Ship and Platiorm Motions. Berkeley, October 1983.

Inglis, R.B.: "A Three-Dimensional Analysis of the Motion of a Rigid Ship in Waves", Ph.D. Thesis, University of London, 1980.

Nethercote, W.C.E., Piggott, S.D., and Savory, M.W.: "SWATM2: A Computer Program for the PredictiOn of SWATH Ship Motions in Regular and Irregular Waves", DREA Tecithical Memorandum 851217, September 1985.

McCreight. K.K. and Lee, C.M.: "Manual far Mono-hull or Twin-Hull Ship Motion Prediction Computer Program", DTNSRDC Report SPD.686-02, June 1976.

Lee, C.M.: "Theoretical Prediction of Motion of Small-Waterplane-Area, Twin-Hull (SWATH) Ship in Waves", DTNSRDC Report 76-004& December 1976.

Salvesen, N., Tuck, E.O., and Faltinsen, 0.: "Ship

Motions and Sea Loads", SNAME Transactions, Vol. 78, 1970, pp. 250-287..

van Wajree, F.: "Resistance Prediction Method for Hydrofoil Craft", MSc Thesis, Technical University Delfi. April 1985.

9 Whicker, L.F. and Fehlner, L.F.: "Free-Stream

Characteristics of a Family of Low-Aspect-Ratio, All-Movable Condol Surfaces for Application to Ship Design',

DTMBReport933, 1958.

McCreight, K.K.: "Assessing the Seaworthiness of SWATH Ships", SNAME Transactions, Vol. 95, 1987, pp. 189-214.

Hooft, J.P.: "Further Considerations on Mathematical Manoeuvring Models", MARIN Publication M50770, March 1987.

Dawson, C.W.: "A Practical Computer Method for Solving Ship-Wave Problems", Proceedings of the Second lnt. COnf. on Numerical Ship Hydrodynamics, Berkeley,

1977.

Hess, J.L. and Smith, A.M.O.: 'Calculation of

Potential Flow about Arbitrary Bodies", Progress in Aeronautical Science, Vol. 8, 1967. pp. 1138.

Raven, H.C: "Variations on a Theme by Dawson: Recent hpmvements of a Potential Flow Calculation Method for Ships, Seventeenth Symposium on Naval Hydrodrodynarnics, The Hague, 1988

Pins, W.C., Nielsen, J.N., and Kaattari, G.E.: "Lift

and Center of Pressure Of Wing-Body-Tail Combinations at Subsonic, Transonic, and Supersonic Speeds:, NACA Report 1307, 1957.

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Table 1 Main particulars

Ni

--.-:-

-Fig. 1 General arrangement

:a

t.1

0----

ffo..US, ____ roso.-o,1o.

ft.

-S S .3

f

- T001

----0

6

-'Coot 0.---0---- IU&oJ '.0 IPVt IN _j5

Fig. S Hull interference, in wave induced forces l.0

/

'1

1'

N-'

,c1'Clo. ,9 0--- 2 --. ,1" 160 350 0 - -,l,0 I10

I-I:

UIWI&T2O9 ITIlSOl. 091? MONITUDI

WIGTU ItIWI P1*PEIIDICULIJ3 LPP U 106.54

IT! 0? IflUTN LI I 12.19

UZ& c?UZ LINt ITtUTSI I N 24.31 ISAü0UT (IVU UNtil ?. 9 9.01

PlIPI&Ci? V11!T N ? 5,246

?U 0? CI&VITT AN0VZIASI ID I 10.56

ETII 0? DTANVT Afl I'.?. LCS N 51.0

L09GXTUDIIIU. ACINTIIC 91109? .

I

16.95

?II9IVflU I1?AC?I1C 11109? III? 9 3 15

&0902709i1&Z. IIbIUS 0? GTh*TT0N k77 9 25.12

Im*IIITIIU OtOIDI OF OTIATION 599 I 12.62

IVIAL lOLL IOD - To I 16.6

TUIAL PIYDI PUIOD TO I 16.9

iAi 11w, PERIOD TI 5 10.2

01 - 1.0 '.3

ocraDcI Ii0'S

Fig. 3 Contributions to wave induced forces

0 0.5 - - 1.0 1.5

IN /3

Fig. 2 Contributions to wave induced forces

I.' U.,

iv- FL'CT IN100/S

Fig. 4 Hull interference in wave induced forces 00.0 S.. 'Soc S 100 0

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2 3

I

vt ror 1w IIIS 2

I

Ii

i.i

tICT Ill

vt-017! lc x IOn !I I1O.I. ZFJICT1OI S

-;'

_'\\TT

$ lOot O1RtCT11 110 10C SS!o ?$ $2I 15Th CI?TIACT1l u

-T0t1y - -lOVt0JOt77) 10?70 X . 2.1 2.0 I

--.--.--- ,c

_i__. I H /?

/\

L'

7--/

/

Sa ..V-. 1.1 I.. ..vt OI07Z o ISa IS prSpsli.r. -70RY -10TT2ICT

II

V

7- --ij :1 $ I'

/

"p

ii

.

\

/

5' a. - --- V

V

V

Fig. 6 Surge excjtation (Hull) Fig. 8 Heave excitation (Hull)

Fig. Sway excitation (Hull) Fig. 9 Pitch excitation (Hull)

LI

Ii

it rXIC5 I,. I?,$

rDCT là 1.1

-

I

A

I

(10)

3.

a

LI

- - - LI

4v rpcy IN /5

Fig. 9a Hull interference in added

- mass (sway)

Fig. 10 Reduced dynamic fin loads

IX

SI .5

FXsCy IS NAOtS

Fig. 11 Reduced -dynamic fin loads

FON PV.q..oy 0.45

PSy 0.

4.'I -ill/I Paq.7 0.X.U.& -0

oir

sTsr

1$st9W P0SITI-1 IN5,.

Fig. 12 Amplitude of the fluctuating angle of attack in percentage

ofthe amplitude of the

undisturbed values 50 IFT rIN - T. 12.0.5. Ia U. laps pp. pa; p

-.-'I.

N. q -. I /

-\\k1ur.\

- -

_._

'1/1.

_:

'N 0.0

aS1,, ri,. - PtED SlOTh 12.5 US 150 U. lisps ItU. p 5

a.

- LI LI S.

(11)

a V b

---0----

--a--If

1I6tRSC POS?l. I..

P1..., O.4 .d/.

0.71 r.dIi

..g,.

a..,

Fig. 13 Amplitude of the fluctuating angle of attack in percentage of the amplitude of the

undisturbed values S S 49. ax 0

Fig. 14 Fin contribution to heave damping

10

HULL HN.

Fig. 15 Pressure contours in calm water (20 knots) POSITION I POSITION 2 POSITION HULL ONL

-Fig. 16 Pressure contours in calm water (20 knots)

r B

Fig. 17 Positions used for angle of attack calculations

1..ft i,o.fi

Sit fin. .-ntt.i

DCL 3.0! n.CI. 6.28 fin nsf'. pin. (aft

-0 IC 90 D IN IlOIS

(12)

05 '0

.t roacn I'. 8 S '#COut'C, I' 0855

Fig. 18 Response of heave Fig. 20 Response of rol.l

n Si..1.irfto 0500 #tSu.T5 I(A5N5 180 IrS. 12.5 II. ici.0 a £ ° SI,cLlrlCo lt5T RSSILTS IC80iui 90 IrS. Y 12.5 'a ,rr,u, a --£ S -0 o 0 £ £ £

£

0 Sl,v.lrIcL TOST 'Slk...' TN 1(85105 90 5(0. 0

--

a :

---:

Fig. 19 Response of heave Fig. 21 Wave elevation due to steady

forward speed of SWATH

00 10 I .0 IC D.LlC, 10 R%S

I

3. 2. J 4

Cytaty

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