1PRADS92, Conf. on Practical Design ofShips and Mobile Structures, Volume I,1992, Newcastle upon Tyne, U.K.Updated: 05-12-2000.Internet:http://dutw189.wbmt.tudelft.nl/~johanhttp://www.shipmotions.nl

Report 0902-P, 1992,Delft University of Technology,Ship Hydromechanics Laboratory,Mekelweg 2, 2628 CD Delft,The Netherlands.E-mail: J.M.J.Journee@wbmt.tudelft.nl

Quick Strip Theory Calculations in Ship Design

J.M.J. JourneDelft University of Technology

Abstract

This paper describes a strip theory based calculation method for ship design purposes, whichdelivers information on ship motions and added resistance within a very short computationtime. The practical sense of using strip theories for this tool is discussed. Comparativevalidations of calculated data with results of the more accurate parent computer program aregiven.

1 Introduction

Generally, ship design is focussed on stillwater performance. In many cases thedesigner also needs information onseakeeping variables such as local motionsor accelerations, added resistance,shipping water and bow slamming. Modelexperiments to obtain this informationduring the ship design process areexpensive, time consuming and notpractical.Since two decades it is possible toincorporate seakeeping considerationsfrom the beginning of the design bynumerical methods. These numericalmethods include linear theories like striptheories up to complete three-dimensionaltheories. Non- linear theories will becomeavailable for design purposes too.Nowadays various ship motion programs,generally based upon linear strip theories,are occasionally used during the ship

design process. The practical sense ofusing strip theories in an early design stageof a ship will be discussed. In an iterativedesign process these programs are oftencomplicated in use and too slow. Thedesigner needs more quick computationaltools which are convenient in use, wellprotected against human input errors andcalculated data which are easy to interpret.For this purpose, a strip theory basedcomputational method has been developed,which delivers the designer this relevantinformation within a very short computingtime. Use has been made of a newlyconstructed database, which contains allrequired information on two-dimensionalpotential hydrodynamic coefficients in thesway, heave and roll mode for a very widerange of mono-hull cross-sections. For thedetermination of these two-dimensionalcoefficients of ship-like cross-sections,these sections are conformally mapped to

2the unit circle by the so-called two-parameter Lewis transformation.The advantage of conformal mapping isthat the velocity potential of the fluidaround an arbitrarily shape of a cross-section in a complex plane can be derivedfrom the more convenient circular cross-section in another complex plane. In thismanner hydrodynamic problems can besolved directly with the coefficients of themapping function.The advantage of making use of the two-parameter Lewis conformal mapping isthat the non-dimensionalised frequency-depending potential coefficients are afunction of two parameters only. Theseparameters are represented by half thebreadth to draught ratio 0H and the areacoefficient s of the cross-section. So, adatabase can be filled with the potentialcoefficients for a sufficient large numberof these parameters.Now the hydrodynamic potentialcoefficients of cross sections of any mono-hull ship can be found by an interpolationin this database. According to the striptheory, the total hydrodynamic coefficientsfor the ship can be found easily byintegrating the sectional values over theship length.For several ship types, calculatedresponses for six degrees of freedom bythis relatively simple tool are comparedwith those obtained by accurate striptheory calculations when using N-parameter conformal mapping techniquesor pulsating sources on the submergedcross section contour of the actual hullform.

2 Application of Ship Motions inShip Design.

Faltinsen and Svensen (1990) havediscussed the incorporation of seakeepingtheories in Computer Aided Ship Design.An overview of seakeeping theories forships is presented and it is concluded that,

nevertheless some limitations, the striptheory is still the most successful andpractical theory for the calculation of thewave induced motions of the ship in anearly design stage of a ship.The strip theory is a slender body theory,so one should expect less accuratepredictions for ships with low length tobreadth ratios. However, experimentsshowed that the strip theory appears to beremarkably effective for predicting themotions of ships with length to breadthratios down to about three.The strip theory is based upon the potentialflow theory. This holds that viscous effectsare neglected, which can deliver seriousproblems when predicting roll motions atresonance frequencies. In practice, viscousroll damping effects can be accounted forby empirical formulas.Because of the way that the forced motionproblems are solved generally in the striptheory, substantial disagreements can befound between the calculated results andthe experimental data of the wave loads atlow frequencies of encounter in followingwaves. In practice, these near zerofrequency of encounter problems can besolved by forcing the wave loads to goartificial to zero.For high-speed vessels and for large shipmotions as appear in extreme sea states,the strip theory can deliver less accurateresults. The strip theory accounts for theinteraction with the forward speed in avery simple way. The effect of the steadywave system around the ship is neglectedand the free surface conditions aresimplified, so that the unsteady wavesgenerated by the ship are propagating indirections perpendicular to the centre planeof the ship. In reality the wave systemsaround the ship are far more complex. Forhigh-speed vessels, unsteady divergentwave systems become important. Thiseffect is neglected in the strip theory.The strip theory is based upon linearity.This means that the ship motions aresupposed to be small, relative to the crosssectional dimensions of the ship. Only

3hydrodynamic effects of the hull below thestill water level are accounted for. Sowhen parts of the ship go out of or into thewater or when green water is shipped,inaccuracies can be expected. Also, thestrip theory does not distinguish betweenalternative above water hull forms.Because of the added resistance of a shipdue to the waves is proportional to thevertical relative motions squared, itsinaccuracy will be gained strongly byinaccuracies in the predicted motions.Nevertheless these remarks, seakeepingprediction methods based upon the striptheory provide a sufficiently good basis foroptimisation studies at an early designstage of the ship.At a more detailed design stage, it can beconsidered to carry out additional modelexperiments to investigate for instanceadded resistance or extreme eventphenomena, such as shipping green waterand slamming.

3 Strip Theory Method

The equations of motions for six degreesof freedom of a sailing ship, influenced byexternal loads, are based upon Newton'ssecond law of dynamics. Because of thesymmetry of a ship, two uncoupled sets ofthree coupled equations of motion can bedistinguished.In a right-handed co-ordinate system, withthe origin in the ships centre of gravity,these equations read as follows:

( ){ }=

=+++6

1jkjkjjkjjkjkj XxCxBxAM !!!

for k = 1, 2, 3, 4, 5, 6where:k = 1, 3, 5: Coupled surge, heave and

pitch motionsk = 2, 4, 6: Coupled sway, roll and yaw

motionsjx!! Acceleration of harmonic oscil-

lation in direction j

jx! Velocity of harmonic oscillation indirection j

jx Displacement of harmonic oscil-lation in direction j

kX Harmonic exciting wave force ormoment in direction k

kjM Solid mass or inertia coefficient

kjA Hydrodynamic mass or inertiacoefficient

kjB Hydrodynamic damping coefficient

kjC Spring coefficientAs a result of this formulation in thefrequency domain, any system influencingthe behaviour of the vessel should have alinear relation with the displacement, thevelocity and the acceleration of the body.The hydrodynamic mass and dampingcoefficients and the external wave loadsare depending on the amplitude and thefrequency of oscillation. The restoringspring coefficients are constant. Tocalculate the hydrodynamic mass anddamping coefficients and the externalwave loads in these equations of motions,several approaches of the strip theory canbe found in literature. Here, use has beenmade of a strip theory method, as has beenincorporated in the recently developedcomputer program SEAWAY by Journe(1990a).SEAWAY is a ship motions computerprogram, suitable for use on a PC or amain frame and based upon the ordinaryand the modified strip theory method, tocalculate wave-induced loads, motions andmechanic loads with six degrees offreedom of mono- hull ships and barges inseaway. The incident wave potential hasbeen defined for a restricted water depth.This holds that the program is suitable forshallow water, with keel clearances downto about half the ships draught. When notaccounting for interaction affects betweentwo individual hulls, the program issuitable for twin-hull ships, such ascatamarans or semi-submersibles, too.

4Potential CoefficientsThe coefficients kjA and kjB of the shipare defined here in a right-handed co-ordinate system with the origin in theship's centre of gravity, the longitudinalaxis forward parallel to the water line andthe vertical axis upwards.The coefficients are derived from the two-dimensional hydrodynamic potentialcoefficients kja and kjb (for jk , = 1,1 2,23,3 4,4 and 2,4 or 4,2) with the co-ordinatesystem in the local water line.For the determination of the two-dimensional coefficients for the sway, rolland yaw motions of ship-like cross-sections, the pulsating source method ofFrank (1967) can be used. This method issuitable for fully submerged cross-sectionstoo. The disadvantage of the method is arelatively large computing time.Results will be obtained much quicker bymapping these cross sections conformablywith N parameters to the unit circle. Theadvantage of conformal mapping is thatthe velocity potential of the fluid aroundan arbitrarily shape of a cross-section in acomplex plane can be derived from themore convenient circular cross-section inanother complex plane. In this manner, thehydrodynamic problems can be solveddirectly with the coefficients of themapping function.Results will be obtained in a shorter timewith the simplest form of conformalmapping, the so-called two-parameterLewis transformation. The advantage ofmaking use of this simple mapping methodis that the non-dimensionalisedhydrodynamic potential coefficients aredepending on two parameters only: thehalf breadth to draught ratio 0H and thearea coefficient s as of the cross section.An elaborate survey of ship hull forms,obtained by Lewis conformal mappingfunctions, is given by Von Kerzeck andTuck (1969).The theory on the calculation of the two-dimensional hydrodynamic potentialcoefficients is given by Ursell (1949) and

Tasai (1961). The total hydrodynamiccoefficients for the sway, roll and yawmotions can be found easily by integratingthe cross sectional values over the shiplength. The pitch and yaw coefficientsfollow from the heave and sway momentsrespectively around the centre of gravity.For the surge motions a separate approachhas to be used. All algorithms aredescribed in detail by Journe (1990b).

Viscous DampingFor surge and roll, additional dampingcoefficients have to be introduced.Because these additional contributions tothe damping are from a viscous originmainly, it is not possible to calculate thetotal damping in a pure theoretical way.A relatively small additional viscous surgedamping has been derived from thederivative to the forward ship speed of theempirical resistance-speed curve of Troost(1955):

23/2 VCR Rsw = or:

VCdV

dRb

R

swv

=

=

3/2

11

2 where:

{ } 6.0log2.156.310 10

3

++=

ppR L

C

with ppL in meters.

The viscous contribution into the total rolldamping is large. Experiments show also astrong non-linear behaviour of some partsof the additional roll damping.For the estimation of the additional rolldamping parts, use has been made of workpublished by Ikeda, Himeno and Tanaka(1978). Their empirical method is calledhere the Ikeda Method and it estimatesthe following components of the additionalroll-damping coefficient of a ship:

( )144sb Linear forward speed correction of

potential damping

5( )144lb Linear lift damping

( )244 fb Non-linear friction damping

( )244eb Non-linear eddy damping

( )244kb Non-linear bilge keel damping

Then the linear and non-linear additionalroll damping coefficients are given by:

( ) ( ) ( )

( ) ( ) ( ) ( )244

244

244

244

144

144

144

kefv

lsv

bbbb

bbb

++=

+=

So, the roll damping term in the left-handside of the equation of motions for rollshould be given by:

( ) ( ) ( )44

2444

144444 xxbxbxb vv

eqv !!!! +=

The non-linear term can't be used infrequency domain equations. However, anequivalent linear additional roll-dampingcoefficient can be found by therequirement that the equivalent lineardamping has to dissipate an equal amountof energy as the non-linear damping.Then the equivalent linear additional roll-damping coefficient ( )eqvb44 becomes:

( ) ( ) ( )2444

14444 3

8vav

eqv bxbb +=

So, this equivalent linear additional rolldamping is depending on the amplitude

ax4 and the frequency of the rollmotion.Ikeda, Himeno and Tanaka (1978) claimfairly good agreements between theirprediction method and experimentalresults. They conclude that the method canbe used safely for ordinary ship forms. Butfor unusual ship forms, very full shipforms and ships with a large breadth todraught ratio the method is not alwayssufficiently accurate.

Wave LoadsIn strip theory calculations, the wave loadson a ship are found by integrating the two-dimensional loads on the cross sections ofa restrained ship over the ship length.These loads consist of a Froude-Krilovpart and a diffraction part.The Froude-Krilov force or moment inwaves can be expanded in series. Thedominating term in the relevant part of theseries delivers equivalent directionalcomponents of the orbital acceleration andvelocity. These components are used byJourne (1991) to calculate the diffractionpart of the wave loads.

Motion CharacteristicsNow two sets of six coupled equations ofmotions with in and out of phase termsbecome available, which can be solved bya numerical method. From these solutionsfollow the frequency characteristics of themotions, which are the motion amplitudeto wave amplitude ratios and the phaselags of the motions relative to the waveelevation at the ship's centre of gravity.With these basic motions, the harmonictranslations in the three directions in anyselected point on the ship can becalculated. The harmonic velocities andaccelerations in the three directions areobtained by taking the first and secondderivatives of the displacements. However,for the accelerations in the longitudinaland lateral direction in a ship-boundedaxes system, a component of theacceleration of gravity has to be added.Harmonic vertical relative displacementswith respect to the undisturbed wavesurface can be obtained too.

Added Resistance CharacteristicsTwo theoretical methods have been usedhere for the estimation of the time-averaged added resistance of a ship due tothe waves and the resulting ship motions: a radiated wave energy method, as

proposed by Gerritsma andBeukelman (1972), used here for headto beam waves and

6 an integrated pressure method, asproposed by Boese (1970), used herefor beam to following waves.

The frequency characteristics are foundby dividing the added resistance by thewave amplitude squared.

Wave Spectra DefinitionsFor a comparison of the calculatedbehaviour of different designs or to get animpression of the behaviour of a specificdesign in a seaway, standardrepresentations of the wave energydistributions are required. Threemathematical definitions with twoparameters of normalised spectra ofirregular unidirectional waves have beenused here: a Neumann wave spectrum, a

somewhat wide wave spectrum, a Bretschneider wave spectrum, also

called ISSC, ITTC or ModifiedPierson-Moskowitz wave spectrum, anaverage wave spectrum and

a mean JONSWAP wave spectrum, anarrow wave spectrum.

These two parameters are the significantwave height and the average wave period.

Statistical Values and ProbabilityDensity FunctionsThe energy spectrum of the motions of asailing ship in irregular waves is obtainedby multiplying the square of the transferfunction of the motions with the waveenergy spectrum. From this spectraldensity function the significant amplitudeof the motions can be calculated. Anaverage period can be defined by thecentroid of the spectrum or the averagezero-crossing period, found from thespectral gyradius. In case of not too widemotion spectra, the probability densityfunctions of the maximum and minimumvalues are given by the Rayleighdistribution. Then the probability ofexceeding a threshold value by theamplitude of the motions and the numberof occurrences per hour can be calculated.

The energy spectrum of the addedresistance is obtained by multiplyingtwice the transfer function of the addedresistance with the wave energy spectrum.From this follows the average addedresistance in irregular waves.

Shipping WaterShipping water is defined by exceedingthe geometrical freeboard by the verticalrelative motions. But the freeboard will beinfluenced by static swell-up, the wavesproduced by the ship sailing in still water.Also an oscillating ship will producewaves it-self, which will change theamplitude of the vertical relative motion.So a dynamical swell-up will beintroduced too. These phenomena are notincluded yet here in the calculation ofshipping water.

Bow SlammingSlamming is a two-node vibration of theship caused by suddenly pushing the shipby the waves. Ochi (1964) has translatedthese vibration phenomena intorequirements for the vertical relativemotions of the ship. He defined bowslamming by an emergence of the bow ofthe ship and exceeding a certain thresholdvalue by the vertical relative velocitybetween the wave surface and the bow ofthe ship. The reference location of thebow along the ship length is defined byOchi at 10 per cent of the length aft of theforward perpendicular. The static anddynamical swell-up are ignored.

4 Quick Strip Theory Calculations

As mentioned in the introduction,nowadays it is possible to use ship motionsprograms based upon the linear striptheory in ship design. In an iterative designprocess, these programs are oftencomplicated in use and too slow. Thedesigner needs much quickercomputational tools which are convenientin use, well protected against human input

7errors and calculated data which are easyto interpret.For this purpose, a strip theory basedcomputational method has been developed,which delivers the designer the relevantinformation within A very shortcomputation time.The major part of expected human inputerrors is related to the input of the offsetsof the hull form of the ship. The major partof the total calculation time will beconsumed by the calculation of thepotential coefficients and the solution ofthe equations of motion. So these partshave to be simplified for the use in adesign process.The risk on offset input errors can beminimised by using the two-parameterLewis conformal mapping method, whichrequires an input of the cross-sectionalwater line breadths, draughts and areasonly. Since the non-dimensional potentialcoefficients are depending then on twocoefficients only, use can be made of adatabase, which contains all requiredinformation on two- dimensional potentialcoefficients in the sway, heave and rollmode for a very wide range of mono-hullcross sections. The ranges of the halfbreadth to draught ratio 0H and the areacoefficient s for the different typicalLewis forms are shown in Figure 1.For practical reasons, only a reducedregion of 0H and s values will beconsidered now. To obtain ship-like Lewisforms, the area coefficient s is boundedby a lower limit to omit re-entrant Lewisforms and by an upper limit to omit non-symmetric Lewis forms: for 0.10

8Based upon computer program SEAWAY,a pre-processing program, namedSEAWAY-Q, has been written. At eachgrid point and frequency, the coefficients

kja and kjb are calculated for jk , = 2,23,3 4,4 and 2,4 or 4,2. The 82,992calculated two-dimensional hydrodynamicpotential coefficients are written to a 400kBytes unformatted file, namedSEAWAY-Q.COF.A new 300 kBytes ship motions program,also based upon program SEAWAY andnamed SEAQUICK, has been written. Thisprogram is valid for conventional mono-hull ships, sailing in deep water. Cross-sectional water line breadths, draughts andareas are input. The program reads theSEAWAY-Q.COF file and a seconddegree Lagrange interpolation routine isused to determine the potential coefficientsof the cross-sections of the ship.To obtain the solutions of the equations ofmotion is computing time-consuming too.In SEAQUICK, the frequency characteris-tics are calculated for a relatively smallnumber of wave frequencies: = 0.1, 0.2,0.3 ....... 1.8 rad/sec.Then, at each frequency interval twoadditional frequency characteristics aredetermined by an interpolation with aTheilheimer polynomial. For a correctcalculation of the wave loads, informationon the underwater hull form of the ship isrequired. Because the actual hull form isnot known, the Lewis hull form has beenused for this.The remaining calculation routines, suchas the determination of the potential surgecoefficients and the viscous effects, thecalculation of the wave loads, the solutionthe equations of motions and the spectralcalculations, are similar to those used inthe parent program SEAWAY.This approach results into a very quickcomputer program that uses less than 10%of the computing time of the parent striptheory program. Nevertheless bulbousbows is not accounted for quite well, theaccuracy is very high when comparing the

results with those of the parent program.This will be shown further on.To obtain a possible further increase of thecalculation speed and the accuracy, thecoefficients in the grid points can bereplaced by Theilhelmer polynomialcoefficients.

5 Comparative Validations

With program SEAQUICK, ship motioncalculations have been carried out here forseveral ship types: a container ship, a crude oil tanker, a trawler and a number of transformed container

ships.The calculated data have been comparedwith those of the parent programSEAWAY, of which the calculations havebeen carried out with high demands on theaccuracy of the calculated data. This holdsconformal mapping of the cross sectionswith 10 mapping coefficients, so 1a , 3a ,......, until 19a , and the use of the Frankmethod for bulbous cross sections.The comparisons are presented here for theordinary strip theory method. So-calledend-terms are included. In thesecomparisons the ships are assumed to sailin bow-quartering seas, with wavescoming from 135 degrees off stern. For thecontainer ships and the crude oil tanker,the calculations have been carried out inOpen Ocean areas and for the trawler inNorth Sea areas. The wave spectra in theOpen Ocean areas are defined by aBretschneider wave spectrum. The wavespectra in the North Sea areas are definedby a mean JONSWAP wave spectrum with

3.3= .Contestable relations between thesignificant wave height 3/1H and thecentroid period 1T of the waves are givenin Table 1.

9Open OceanAreas

North SeaAreasBF

3/1H(m)

1T(s)

3/1H(m)

1T(s)

1 1.10 5.8 0.50 3.5 2 1.20 5.9 0.65 3.8 3 1.40 6.0 0.80 4.2 4 1.70 6.1 1.10 4.6 5 2.15 6.5 1.65 5.1 6 2.90 7.2 2.50 5.7 7 3.75 7.8 3.60 6.7 8 4.90 8.4 4.85 7.9 9 6.10 9.0 6.10 8.810 7.45 9.6 7.45 9.511 8.70 10.1 8.70 10.1

Table 1 Assumed Relations of WaveEnergy Spectra

For each ship, the accelerations in thethree directions have been calculated inselected points on the ship defined by:- 75% of ppL forward of the aft perpen-

dicular- 75% of half the breadth from the centre

line to port side- 50% of the amidships draught above

the load water line.For each ship, bow slamming is defined at10% of ppL aft of the forward perpen-dicular. The added resistance due to theship motions in waves has been calculatedwith the radiated energy method.

Container ShipAs an average seagoing vessel, the S-175Container Ship Design with a length of175.00 meters has been chosen for thisvalidation study. Elaborate comparativeresults on experiments and calculations ofthat ship have been published by theSeakeeping Committee of the ITTC andmany others. The calculations have beencarried out here for a sustained ship speedof 16.1 knots ( 20.0=Fn ). The viscousroll damping has been determined by theIkeda method.

Crude Oil TankerAs a very large ship, a 200,000 tons dead-weight tanker with a length of 310 meterhas been chosen. The calculations havebeen carried out for a sustained ship speedof 15 knots. The non-dimensional totalroll-damping coefficient has been fixed to

075.0= .

TrawlerAs a very small ship, a 30.60 m lengthtrawler has been chosen. The calculationshave been carried out for a sustained shipspeed of 8 knots. The non-dimensionaltotal roll-damping coefficient has beenfixed to 050.0= .

Validations with Three Ship TypesIn Figure 2, a comparison of the calculatedacceleration, added resistance and bowslamming phenomena has been given.

Figure 2 Comparison of Calculated Dataof a Container Ship, a Crude Oil Tanker

and a Trawler

In all sea states a good agreement has beenfound. Some small deviations in high seasare caused by using a Lewis hull forminstead of the actual hull form, whencalculating the sectional Froude-Kriloyloads and equivalent orbital accelerations.Because the ships were fully loaded, onlyfor the containership bow slammingappeared in the calculated data.

Validations with TransformedContainer ShipsFor the S-175 Container Ship, some of thehull form parameters have been variedextremely to investigate the accuracy of

10

calculated trends of motions of alternativeship designs, sailing with 20.0=Fn in asea state defined by Beaufort 8. Thelongitudinal position of the centre ofbuoyancy LCB and the block-coefficient

bC have been varied by a transformationmethod for ship hull forms, as developedby Versluis (1977). The size of the shiphas been varied by linear scaling of thethree-dimensional hull form with multi-plication factors .

50.150.004.004.0

015.0015.0

00

00

+

+

bbb

pppp

CCCLLCBLCBLLCB

In Figure 3, a comparison of the calculatedacceleration and added resistance has beengiven. According to the calculations, inthis sea state no bow slamming appears.

Figure 3 Comparison of Calculated Dataof Several Transformed S-175 Container

Ship Designs

Again, a very good agreement between thetwo calculation methods has been found.Figure 3 shows too that, within practicalregions for the location of the centre ofbuoyancy and for the block-coefficient, nosignificant reductions of the accelerationsin the selected point and the addedresistance will be achieved. For this, theship's size appears to be a more importantparameter. However, an optimisation studyis not the aim of this paper.

6 Conclusions

Based upon the validations, it is expectedthat this simple calculation method can beused safely for conventional mono-hullships, at least in a preliminary design stageof a ship.However, a few restrictions have to bemade here:- For high-speed vessels, for ships with

length to breadth ratios lower than 3.0and for ships with a significantinfluence of submerged cross-sectionsor bulbous bows, more or lessinaccurate results can be expected.

- Because of using a linear theory, lessaccurate results can be expected forlarge motions in extreme seaconditions.

- The method is based upon Lewisconformal mapping of the cross-sections. This holds that sections withdifferent shapes, but with an equalbreadth, draught and area, will receiveequal values for the two-dimensionalhydrodynamic potential coefficientsand wave loads.

- When calculating vertical motionsrelative to the waves or calculatingprobabilities on shipping water or bowslamming, the static and dynamicalswell-up is not accounted for.

- The method of Ikeda to estimate theviscous roll damping is less suitablefor an unusual ship form, very fullships or ships with a large breadth todraught ratio. But, estimated orexperimental roll damping coefficientscan be input too.

- The calculation method is used herefor an infinite water depth. Restrictedwater depth effects are not included.

When more accurate results are required,use has to be made of strip theoryprograms like the parent program.However, some of these restrictions arerelated to the strip theory method it-self. Inthat case one is dependent on othercomputing techniques or modelexperiments.

11

7 References

Boese (1970)P. Boese, Eine Einfache Methode zurBerechnung der Widerstandserhhungeines Schiffes in Seegang, Institt frSchiffbau der Universitt Hamburg,Bericht 258, 1970.

Faltinsen and Svensen (1990)O. Faltinsen and T. Svensen, Incorpo-ration of Seakeeping Theories in CAD,Proceedings of the InternationalSymposium on CFD and CAD in ShipDesign, Maritime Research InstituteNetherlands, Wageningen, The Nether-lands, September 1990.

Frank (1967)W. Frank, Oscillation of Cylinders in orbelow the Free Surface of a Fluid, NavalShip Research and Development Center,Washington, U.S.A., Report 2375, 1967.

Gerritsma and Beukelman (1972)J. Gerritsma and W. Beukelman, Analysisof the Resistance Increase in Waves of aFast Cargo Ship, International Ship-building Progress, Vol. 18, No 217, 1972.

Ikeda, Himeno and Tanaka (1978)Y. Ikeda, Y. Himeno and N. Tanaka, APrediction Method for Ship Rolling,Department of Naval Architecture,University of Osaka Prefecture, Japan,Report 00405, 1978.

Journe (1990a) J.M.J. Journe, SEAWAY-DELFT, UserManual and Theoretical Background ofRelease 3.00, Delft University ofTechnology, Delft ShiphydromechanicsLaboratory, The Netherlands, Report 849,January 1990.

Journe (1990b)J.M.J. Journe, Theory and Algorithms ofTwo-Dimensional Hydrodynamic PotentialCoefficients, Delft University of Techno-logy, Ship Hydromechanics Laboratory,

Delft, The Netherlands, Report 884,November 1990.

Journe (1991)J.M.J. Journe, Motions of RectangularBarges, 10th OMAE Conference, ASMEPaper OMAE-91-367, June 23-28, 1991,Stavanger, Norway.

Ochi (1964)M.K. Ochi, Prediction of Occurence andSeverity of Ship Slamming at Sea,Proceedings of the 5th 0.N.R. Symposium,Bergen, Norway, 1964.

Tasai (1961)F. Tasai, Hydrodynamic Force andMoment Produced by Swaying and RollingOscillation of Cylinders on the FreeSurface, Research Institute for AppliedMechanics, Kyushu University, Japan,Vol. IX, No 35, 1961.

Troost (1955)L. Troost, A Simplified Method forPreliminary Powering of Single ScrewMerchant Ships, New England Section ofthe Society of Naval Architects andMarine Engineers, October Meeting, 1955.

Ursell (1949)F. Ursell, On the Rolling Motion ofCylinders in the Surface of a Fluid,Quarterly Journal of Mechanics andApplied Mathematics, Vol. II, 1949.

Versluis (1977)Versluis, Computer Aided Design ofShipform by Affine Transformation,International Shipbuilding Progress, Vol.24, No 274, June 1977.

Von Kerzeck and Tuck (1969)C. von Kerzeck and E.O. Tuck, TheRepresentation of Ship Hulls byConformal Mapping Functions, Journal ofShip Research , Vol. 13, No 4, 1969.

Delft University of TechnologyAbstract3Strip Theory MethodWave LoadsMotion CharacteristicsAdded Resistance CharacteristicsWave Spectra DefinitionsShipping WaterBow Slamming

4Quick Strip Theory Calculations5Comparative ValidationsContainer ShipCrude Oil TankerTrawlerValidations with Three Ship Types6ConclusionsWhen more accurate results are required, use has to be made of strip theory programs like the parent program. However, some of these restrictions are related to the strip theory method it-self. In that case one is dependent on other computing techniques7References