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ISP, Volume 23, No. 265, 1976.Updated: 13-09-2001.

Internet:http://dutw189.wbmt.tudelft.nl/~johanhttp://shipmotions.nl

Report 0427-P, 1976,Delft University of Technology,Ship Hydromechanics Laboratory,Mekelweg 2, 2628 CD Delft,The Netherlands.E-mail: J.M.J.Journee@wbmt.tudelft.nl

Prediction of Speed and Behaviour of a Ship in a Seaway

J.M.J. Journée

Delft University of Technology

Summary

A computer program has been developed to calculate speed and behaviour of a ship in aseaway. In this stage the program is suitable for seagoing vessels in head waves. Indetermining the speed, two factors are considered: the natural speed reduction due to addedresistance caused by wind and waves and the voluntary speed reduction by the ship's captain,in order to prevent severe motions.

1 Introduction

For almost twenty years now, a ship'scaptain can make use of routing advisesfrom weather routing departments like thatfrom the K.N.M.I. (Royal NetherlandsMeteorological Institute) at De Bilt [1].With a known rough weather pattern in theocean an optimum ship’s route can befound with a minimum travelling time,fuel consumption or risk of damage of theship and its cargo. These routing advises,are based on the momentary and expectedwind and waves and the ship’s reaction tothem. The forecast of wind and waves is ameteorological problem. Up to now theprediction of the behaviour of a ship in aseaway - especially the ship’s speed - isbased on routing experience with the shipconsidered or similar ships.

When routing a ship for the first time arouting officer needs reliable speed lossgraphs, to read the ship’s speed as afunction of wave height and mean wavedirection. Developments in the last decademade it possible to calculate withsufficient accuracy the speed in still waterand the natural speed reduction due toadded resistance caused by wind andwaves. At this theoretical speed dangerousmotions can arise for the safety of crew,ship or cargo. Then the master willvoluntarily reduce speed in order toprevent severe motions. Several criteria forthis decision can be found in literature.At the Ship Hydromechanics Laboratoryof the Delft University of Technology amethod has been developed to calculatethe natural speed, the voluntary speedreduction and the behaviour of the ship at

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this speed in a seaway with head waves.This method has been worked out into anAlgol’60 computer program, namedROUTE, which enables a practical use.

2 Calculation of Speed

Apart from wind and sea conditions, thespeed of a ship in a seaway mainlydepends on three aspects:- dimensions and form of the ship's hull

and superstructure,- dimensions and characteristics of the

propeller and- output and characteristics of the

propulsive machinery. The energy flow of a ship in operation isgiven in the following scheme.

The propeller behind a ship is consideredas an energy transformer: torque with rpmwill be transformed into thrust with a meanspeed of advance. At a certain steam orfuel inlet ratio of the engine there will beequilibrium between the number ofrevolutions and the ship’s speed. Thisequilibrium is in such a way that twoconditions are fulfilled: the torque neededby the propeller must be in equilibriumwith the torque delivered by the engineand the thrust delivered by the propellermust be in equilibrium with the totalresistance of the ship.These two conditions of equilibrium areshown in two coupled equations asmentioned below:

( ) ( )

( ) ( )( ){ }nVt

nVTTHVVR

nVQncnQQ

aWWT

m

am

,1,,,,,,

,,,,

3/1

00

−⋅⋅=

=

µα

η

where the relation between aV and V isgiven by:

( ){ }VwVVa −⋅= 1

At a certain engine setting these twoequations are solved in the programROUTE for every wind and sea conditionas shown in Figure 1.

Figure 1 Scheme of Speed Calculation

For a number of ship speeds the relationsbetween torque needed by propeller andrpm are calculated from the torquecharacteristics of the propeller behind theship and an adapted wake fraction. Therelation between torque delivered by theengine to the propeller and rpm is knownfrom engine characteristics and shaftlosses. These relations give a relation ofequilibrium for speed and rpm, whichtogether with the thrust characteristics ofthe propeller behind the ship and a thrustdeduction fraction results in a resistance,which can be achieved by propeller andengine, as a function of the ship’s speed. Ifthe total resistance of the ship for anumber of speeds is known by calculationthe actual speed of the ship can be found.

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Some parts needed for the determinationof the speed are discussed in the followingparts of this chapter.

2.1 Resistance

The total resistance of a ship in a seaway isdivided into three parts:- still water resistance: ( )VRSW

- wind resistance: ( )WWW VVR α,,- added resistance due to waves:

( )µ,,, 3/1 THVRAW

So the relation between resistance andthrust can be written as:

( ) ( )( )

( ) ( ){ }nVtnVTTHVR

VVRVR

a

AW

WWWSW

,1,,,,

,,

3/1

−⋅==+

++

µ

α

The determination of these three com-ponents of the resistance is given in moredetail in the following paragraphs.

2.1.1 Still Water Resistance

In literature several methods have beendescribed to determine the still waterresistance of a ship. These methods havebeen based on the results of a largenumber of model experiments and full-scale experiments which have beensystematically or statistically transformedinto graphs, tables or empirical formulas.Up to now in the computer programROUTE, one of the next two methods canbe used:• The method of the Shipbuilding

Research Association of Japan [2].This method has been developed forfast slender ships with a block-coefficient between 0.55 and 0.65. It isa great advantage of this method that itcan be used for different loadingconditions of the ship.

• The method of Lap [3] with anextension of Auf ‘m Keller [4]. This

method can be used for most normaland full ships in full load condition.With less accuracy a ship in light loadcondition can be considered as a shipin full load condition with a largebreadth - draught ratio.

Both methods are valid for single-screwships with a limited speed range. For toolow a speed the resistance is extrapolatedwith a second-degree polynomial and fortoo high a speed with a third degreepolynomial. No allowances are made forfouling or a bulbous bow. In the programhowever, it is possible to multiply the stillwater resistance with a correction factor.

2.1.2 Wind Resistance

For containerships and ships in ballastcondition the wind resistance often is apart of the total resistance which may notbe neglected. Isherwood [5] has analysedthe results of wind resistance experimentscarried out at different laboratories withmodels covering a wide range of merchantships. He gives empirical formulas fordetermining the two horizontalcomponents of the wind force and thewind-induced yawing moment on anymerchant ship form for a wind from anydirection. The formula and thecorresponding coefficients for the windresistance are used in the program.

2.1.3 Added Resistance due to Waves

To calculate the added resistance of a shipin a seaway a computer program, namedTRIAL, is available at the Delft ShipHydromechanics Laboratory. An earlierversion of the program has been describedin [6].The ship is considered to travel inunidirectional head waves and only pitchand heave motions are determined. Addedmass and damping for the ships cross-sections are calculated by using a Lewis

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conformal transformation. The resulting fitto the actual cross sectional form issatisfactory for the present purpose [7].The increase of resistance in regular wavesis calculated with the method of Gerritsmaand Beukelman by determining theradiated energy of the damping waves asdescribed in [8].The calculation in an irregular sea is basedon the superposition principle for thecomponents of the wave, motion andresistance spectra as well as on theassumption of linearity for the ship’sresponse. In regular waves the addedresistance varies as the square of the waveamplitude. In a wave spectrum the meanadded resistance would then be calculatedfrom:

( ) ( ) eeea

AWAW dS

RR ωωω

ζ ζ ⋅⋅= ∫∞

022

The program TRIAL has been adapted tothis special problem in the programROUTE. For the description of the seasurface two parameter Pierson-Moskowitzwave spectra are used. For each wavespectrum, the mean added resistance iscalculated as a function of the ship’sspeed.

2.2 Propeller Characteristics

Thrust and torque of an open-waterpropeller are defined by:

25

24

nDKQnDKT

Q

T

ρρ⋅=

⋅=

The coefficients TK and QK aredepending on the number of propellerblades, blade area ratio, pitch ratio andadvance coefficient which is defined by:

nDVJ a=

Propeller characteristics can be obtainedfrom open-water test results of theWageningen B-series propellers, which are

frequently used in practice. At presentabout 120 propeller models of the B-serieshave been tested at the Netherlands ShipModel Basin.The thrust and torque coefficients areexpressed by Oosterveld and VanOossanen [9] as polynomials in thenumber of propeller blades, blade arearatio, pitch ratio and advance coefficient.With the aid of a multiple regressionanalysis the significant terms of thepolynomials and the values of thecorresponding coefficients are determined.The polynomials are valid for open-waterpropeller models with Reynolds number

6102 ⋅=Rn .Oosterveld and Van Oossanen [10] alsogive polynomials to correct thrust andtorque coefficients for the actual Reynoldsnumber of the full-size B-series open-water propeller. These polynomials areused in the program.For the propeller behind a ship thecalculated torque must be corrected forthis behind condition:

ship behind

open water

QQ

R =η

For single-screw ships 1.04 is a good meanvalue for this relative rotative efficiency,while for twin-screw ships 0.97 is advised.

2.3 Wake and Thrust Deduction

In the program, the wake fraction and thethrust deduction fraction can be estimatedby very simple formulas. If one of thesevalues is known, for instance from modeltests, it is also possible to make use of thisvalue.

Wake fraction:• Taylor [11]

single-screw ship:bCw ⋅+−= 50.005.0

twin-screw ship:bCw ⋅+−= 55.020.0

• Harvald [12]

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single-screw ship:( )form hull ,/,/, LDBLCww b=

twin-screw ship:( )BLCww b /,=

• A given value of the wake fraction.

Thrust deduction fraction:• Weingart:

single-screw ship:

⋅+⋅−⋅= b

wp

b CCCwt 50.130.257.1

twin-screw ship:

⋅+⋅−⋅= b

wp

b CCC

wt 50.130.267.1

• A given value of thrust deductionfraction - wake fraction ratio.

• A given value of the thrust deductionfraction.

The above mentioned values are valid instill water. Model tests in still watershowed that wake fraction and thrustdeduction fraction are practicallyindependent of speed. It can be shownfrom overload tests in still water that at anincreasing propeller loading and a constantnumber of revolutions, the wake fractionkeeps constant and the thrust deductionfraction is approximately linearlydecreasing with the model speed.Experiments at the Delft University ofTechnology with a model of a fast cargoship showed no difference between stillwater and regular waves for both fractionsat the same average loading of thepropeller [28].

2.4 Engine Characteristics

For solving the equation between theneeded and delivered torque at thepropeller it is necessary to know therelation between torque and rpm of theengine at a certain steam or fuel inlet ratio.

In this connection two important types ofengines for ship's propulsion aredistinguished.

2.4.1 Turbine

Usually it is accepted that at an increasingengine loading and a constant enginesetting the power remains constant. Thismeans a hyperbolic relation betweentorque and number of revolutions:

nnQcQ m

00 ⋅⋅⋅= η

According to some authors like Geislerand Siemer [13] and Goodwin et. al. [14]in practice there is a linear relationbetween torque and number of revolutions:

( )

⋅−−⋅⋅⋅=0

0 1nnaaQcQ mη

where the coefficient a depends on thetype of the turbine:

0.30.2 −=aIf one takes into consideration that thenumber of revolutions of the propeller of aship in a sea-way will not reduce morethan 10-15 percent at a constant steaminlet ratio, the assumption of a constantpower is sufficiently accurate forcalculating the ship’s speed. The relationsbetween torque and rpm mentioned aboveare shown in figure 2.

Figure 3 Torque – RPM Relation ofa Turbine

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2.4.2 Diesel Engine

For a diesel engine it is mostly acceptedthat at an increasing engine loading and aconstant engine setting the torque remainsconstant. This means that 0.1=a in thelast equation and so:

0QcQ m ⋅⋅= ηIn practice there is some difference withthis assumption. At a constant enginesetting and an increasing engine loadingthe torque will increase first, then obtains amaximum value and afterwards willdecrease again. This can be approximatedby a linear relation between torque andnumber of revolutions, provided that thenumber of revolutions will not reducemore than 10-15 per cent. Then the lineartorque-rpm relation can be used with forinstance 5.1=a . These relations betweentorque and number of revolutions areshown in Figure 3.

Figure 3 Torque-RPM Relation for aDiesel Engine

3 Calculation of Motions

The program TRIAL, mentioned before,calculates vertical absolute and relativemotions in regular waves for different shipspeeds. Ship motions in an irregular seaare determined by linear superposition ofthe ship responses to the individual regularwave components.

Figure 4 Symbols and Definitions

Let us consider the heave motion as anexample for the calculating method. Thedefinitions and symbols are shown inFigure 4.In a complex notation the heave motion inregular waves can be written as:

( ) ( ) ( )ζεωζ ωζ zeti

eza eHtz +⋅⋅=where

( ) ( )ea

aez

zH ω

ζωζ =

defines the response function of the heavemotion. The superposition principleenables the calculation of the variance ofthe heave motion in a known wavespectrum:

( )∫∞

⋅=0

0 eezz dSm ωω

where( ) ( ) ( )eezez SHS ωωω ζζ ⋅=

2

defines the heave spectrum.For most practical applications it may beassumed that motion, velocity andacceleration amplitudes follow theRayleigh distribution law. In this examplethe probability that the heave amplitudeexceeds a certain value *

az is given by:

{ }( )

z

a

mz

aa ezz 0

2*

2*Pr−

=>

The occurrence rate for this per hour willbe:

7

{ } { }z

zaaaa

mm

zzzzN

2

0

**

2

3600Pr⋅

⋅>=>π

in which the second moment of the heavespectrum is given by:

( )∫∞

⋅⋅=0

22 eeezz dSm ωωωζ

The significant amplitude of the heavemotion is given by:

za mz 03/1 2 ⋅=

In this way the program TRIAL calculatesthe significant amplitudes of heave, pitch,absolute and relative motions andaccelerations and the probability andnumber per hour of exceeding a certainvalue by the relative motion.

3.1 Relative Motions

Neglecting the wave disturbance by theship the relative motion at a longitudinaldistance bx from the centre of gravity isgiven by:

θζ ⋅+−= bx xzsb

where bxζ is the vertical wave displace-

ment at position bx .Significant amplitudes and probabilities ofexceeding a given value are calculated asshowed for the heave motion. Because ofbow waves and sinkage due to the ship’sspeed, the effective freeboard ef at thebow generally differs from the geometricfreeboard f .Tasaki [15] gives an empirical formula forthis static swell-up at the bow:

275.0 FnLLBfff

ee ⋅⋅⋅=−=∆

with L is the ship length and eL is thelength of entrance of the water line.Experiments at the Delft ShipHydromechanics Laboratory with a modelof a fast cargo ship in full load and inballast condition has shown a remarkably

good agreement between the measure-ments and this empirical formula. Forcalculating the probability of deck wetnessat the forward perpendiculars thegeometrical freeboard is decreased withthe static swell-up obtained from Tasaki'sformula.Generally, the probability of slammingwill be calculated at station 17 or 18. It isassumed that the static swell-up at thesestations is zero at the instant of re-entry ofthe forefoot in the water in case ofslamming.Dynamic phenomena increase theamplitude of the relative motion at thebow; there is a dynamic swell-up. Whenthe bow immerses, the water surface willrise and when the bow emerges, the watersurface will fall. Tasaki [15] has carriedout forced oscillation tests with a towedship model in still water to measure thedisplacement of the water surface relativeto the bow of the model. From the resultsof these experiments he has obtained anempirical formula to estimate the dynamicswell-up at the bow:

eb

a

a

gLC

ss ω⋅⋅

−=

∆3

45.0

with the restriction:80.060.0 << bC

So the amplitude of the relative motion atthe bow is:

∆+⋅=

a

aaa s

sss 1*

This formula is used in the program forcalculating the probability of shippingwater at the forward perpendiculars.

Van Sluys and Tan have carried outexperiments in regular waves [16] withcompact frigates that have shown that thewave amplitude along the ship’s hull isinfluenced by a factor between 0 and 2.The highest dynamic swell-up appeared inthe neighbourhood of station 17 or 18.Also, experiments at the Delft ShipHydromechanics Laboratory have shown

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here a dynamic swell-up of roughly doublethe value of the dynamic swell-up at thebow. For calculating the probability ofslamming it is assumed that the dynamicswell-up at station 17 or 18 is double thevalue of Tasaki at the bow. Moreinvestigations are necessary to estimate agood mean value.

3.2 Accelerations

The absolute motion at a longitudinaldistance bx from the centre of gravity canbe expressed in heave and pitch motionsby:

θ⋅−= bxzv

The response function of the absolutemotion is:

( ) ( )bea

abev x

vxH ,, ω

ζωζ =

which also can be used for calculating theresponse function of the accelerations atposition bx by:

( ) ( ) 2,, ebevbev xHxH ωωω ζζ ⋅=!!

The variance of the accelerations in a wavespectrum and the Rayleigh distributiongives the probability of exceeding a certainvalue by the amplitude of the acceleration:

{ }( )

v

a

mv

aa evv !!

!!

!!!! 0

2*

2*Pr−

=>

It is also possible to determine theprobability of exceeding a certain value bythe significant amplitude of theacceleration.As Ochi and Motter have shown in [17],the probability expression:

{ } bava ≤>3/1Pr !!

is the same expression as:

bbava ≤

⋅−⋅⋅≥ ln2

21Pr !!

This expression will be used in chapter 4.

4 Voluntary Speed Reduction

When a ship encounters a severe storm theship’s captain will reduce speed in order toease severe motions.

The most important phenomena for thisdecision are the probability of occurrenceand severity of:

1. Deck wetnessCaused by shipping water, this willhappen if the relative motion of thebow exceeds the effective freeboardforward. The probability of deckwetness is expressed by:

{ } s

e

mf

e 0

2

2ssdeck wetnePr−

=in which sm0 includes the dynamicswell-up.

2. SlammingSlamming is a phenomenon associatedwith extreme ship motions in waves.At certain ship speeds in rough seas,the forefoot of the ship emerges fromthe water as a result of large pitch andheave motions and violently impactsthe water surface as it re-enters. Theship's forward bottom thereby sustainsa heavy impulsive pressure from thewater and this impulsive forceproduces a shudder throughout thehull.According to Ochi [18] the probabilityof occurrence of slamming is the jointprobability that the bow emerges andthat the relative velocity exceeds acertain magnitude at the instant of re-entry. He found a critical relativevelocity between the bow and waves,below which slamming does not occurand recommends as a good thresholdvalue:

Lgscr ⋅⋅= 093.0!

The probability of slamming isexpressed by:

{ }

+−

= s

cr

s ms

mT

e !

!

0

2

0

2

22slammingPr

9

in which osm and sm !0 include thedynamic swell-up.

3. Propeller racingThe time-dependent immersion of thepropeller results in a fluctuating torqueand thrust of the propeller. Althoughthe rpm governors greatly reducepossible damage to the propellingmachinery due to racing, large torqueand thrust fluctuations are observed inwaves, even at constant rpm.Aertssen [19] analysed a lot of full-scale trials and defined for propellerracing: there is racing - or the propellerwill be called emergent - on everyoccasion when the decrease of torqueis in excess of 25 per cent. Neglectinga static and dynamic swell-up at thestern, Fukuda [22] has adoptedoccurrence of propeller racing whenthe propeller emergence exceeds one-third of the diameter of the propeller.

4. AccelerationsToo high accelerations can also be areason to reduce speed. The magnitudeof the accelerations is stronglydependent on the ship’s length.Aertssen [20] measured on the trawler“Belgian Lady” even accelerations of

g⋅75.2 at the forward perpendiculars.Gerritsma showed the same in [21].

In [17] Ochi and Motter distinguish, forthe estimation of a limit below which novoluntary speed reduction is expected, twoloading conditions:

1. Full load conditionIn this condition voluntary speed reductionis depending on deck wetness andaccelerations at the bow:

07.0

4.0exceed

willacc. bow of

ampl. sign.

and/or

20Station atwetnessdeck

Pr ≤

⋅

g

2. Light load conditionSlamming at station 17 and bowacceleration are in this conditionreasons for voluntary speed reduction.

03.0

4.0exceed

willacc. bow of

ampl. sign.

and/or

17Station atimpactslam

Pr ≤

⋅

g

Relative motion and velocity are bothnormal random processes, so they aretreated as statistically independent.

For two statistical independent events Aand B may be written:

{ }( ) ( ){ }{ } { }AA

BABA

not Prnot Pr0.1 not and/or not Pr0.1

and/or Pr

⋅−=−==

So the probability function:{ } cBA ≤and/or Pr

may be written as:{ } { } cAA −≥⋅ 0.1not Prnot Pr

As mentioned in Section 3.2, theprobability expression with significantacceleration amplitude can be expressed inthe amplitude of this acceleration and thetwo criteria of Ochi and Motter can beexpressed as follows:

• Full load condition:( )

93.011 0

2

0

2

24612.0

2 ≥

−⋅

−

⋅−−

vs

e

mg

mf

ee !!

10

• Light load condition:( )

97.011 0

2

0

2

0

2

25296.0

22 ≥

−⋅

−

⋅−

+−

vs

cr

s mg

ms

mT

ee !!!

!

These two conditions are used in theprogram ROUTE

5 Practical Applications

In the following parts of this Chapter adescription of the data input in theprogram is given with a discussion aboutsea and wind conditions. For six ships,calculation results are compared with full-scale measurements. The time used by anIBM 370/158 system, like that of theMathematical Centre of the DelftUniversity of Technology, for calculatingspeed and motions in a seaway is abouttwo minutes for one loading conditionwith a memory use of about 400 Kbytes.

5.1 Description of Data Input

The program needs much informationabout the ship. To show this, the data inputfor a fully loaded ship is given here:- text card with 80 symbols including

spaces- length at design waterline- length between perpendiculars- distance from ordinate zero until APP- ratio between gyradius and length

between perpendiculars- estimated service speed- even number of ordinate intervals- even number of waterline distances- number of wave and wind directions- number of points for which relative

motions will be calculated- number of wave spectra and wind

speeds- number of power inputs- array with ordinate distances from

ordinate zero until forward

- from ordinate zero until forward, forevery ordinate:- ordinate number- array with half widths of the

section at the waterlines from keeluntil load waterline

- array with waterline distances ofthe section from keel until loadwaterline

- array with positions with respect toordinate zero of the points for whichrelative motions, shipping water,slamming and acceleration forwardwill be calculated

- array with z -values for calculating theprobability of exceeding, shippingwater and slamming (above loadwaterline is positive)

- array with wave directions (headwaves is 180 degrees)

- array with absolute wind directions(head wind is 180 degrees)

- array with significant wave heights- array with average wave periods- array with absolute wind speeds- length overall- lateral projected wind area- transverse projected wind area- length of perimeter of lateral projected

wind area excluding waterline andslender bodies such as masts andventilators

- number of distinct groups of masts orking posts seen in lateral projection

- type of estimation method of the stillwater resistance:- 1 = method of Lap and Auf 'm

Keller- 2 = method of Shipbuilding

Research Association of Japan- multiplication coefficient for correc-

ting the calculated still water resistancefor a bulbous bow, fouling, etc

- type of estimation method of the wakefraction:- 1 = method of Taylor- 2 = method of Harvald- 3 = a given value of w

- if type = 3 : value of w

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- type of estimation method of the thrustdeduction fraction:- 1 = method of Weingart- 2 = a given value of wt /- 3 = a given value of t

- if type = 2: value of wt /- if type = 3: value of t- relative rotative efficiency- number of propellers- number of propeller blades- diameter of propeller- blade area ratio- pitch ratio- boolean: English horsepower

(1 hp = 76 kg m/sec)- for every input of power:

- type of machine:1 = power is constant2 = torque-rpm is linear

- steam or fuel inlet ratio- mechanical efficiency of the shaft

bearings- power in design condition- rpm in design condition- if type = 2 : linear coefficient

of torque-rpm relation- boolean: ballast condition- if this boolean is true:

- change of draught at ordinate zero- change of draught forward- ratio of gyradius and length

between perpendiculars.

The dimensions of the different values are:length: metertime: secondspeed: knotspower: horsepowerangle: degree

5.2 Sea and Wind Conditions

The recommendations of the twelfthI.T.T.C., Rome, 1969, are used for thedescription of sea and wind conditions.The wave spectra are defined by:

( ) 4

5ω

ζ ωω

B

eAS−

⋅=

in which:ω wave frequency andA , B coefficients.

If statistical information is available on thecharacteristic wave period T and thesignificant wave height 3/1H , a two-parameter spectral formulation can be usedby defining:

4

23/1173

T

HA ⋅= and 5

691

TB =

in which:

2

0

03/1

2

4

mm

T

mH

⋅=

⋅=

π

This period is based on the spectral centreof gravity and it can be taken as theobserved period. The spectral formulation,mentioned above, is used in the program.

If the only information available is thesignificant wave height, the 12th ITTC re-commends for the coefficients A and B :

78.0=A and 23/1

11.3H

B =

This means in the two-parameter spectralformulation a relation between significantwave height and characteristic waveperiod:

3/86.3 HT ⋅=

The 12th ITTC also recommends a relationbetween wind speed and significant waveheight in an open ocean when no data areavailable:

WV 3/1H(kn) (m)20 3.0530 5.2540 8.1050 11.1560 14.65

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5.3 Calculations and Full ScaleMeasurements

For six ships calculation results ofprogram ROUTE are compared with full-scale measurements: 4 ships with a dieselengine and 2 ships with a turbinepropulsion plant. The main dimensions ofthese ships are shown in Table 1.Only measurements in head waves( 00 180150 ≤≤ µ ) are observed to com-pare them with calculations of thebehaviour of these ships in head wind andwaves ( 0180 ).In calculating the wave spectra the relationbetween significant wave height andaverage wave period is defined by:

3/186.3 HT ⋅=as mentioned before. The correspondingwind speed as recommended by thetwelfth I.T.T.C. is used.

It may be noted that differences betweenpredictions and measurements, apart frompossible disagreements between theoryand practice, can be caused by differentreasons. All measurements have a certainerror depending on measuring techniquesand accuracy of the measuring equipment.There is always a difference between theactual wave spectrum and the wavespectrum derived from a spectralformulation with a measured, estimated orassumed significant wave height andaverage wave period. The input values inthe program, like engine settingcorresponding to a certain torque or power,wave direction, wind direction and windspeed are mean values. Deviations fromthese mean values result in differencesbetween predicted and measured beha-viour of the ship.

Table 1 Main Dimensions of Comparing Ships

13

Firstly the calculation results for the fourships with a diesel propulsion plant will bediscussed and after that the results for thetwo ships with turbine propulsion plant.In the last two decades, Aertssen hascarried out experiments with several shipsto study the behaviour of these ships in aseaway. The measurement results of 4ships are used to compare them with thepredictions in head waves:

m.s. Lukuga [23]m.s. Lubumbashi [24, 25]m.s. Jordaens [19]m.s. Dart Europe [26].

The first three ships are conventionalcargo liners and the last one is acontainership, all owned by theCompagnie Maritime Belge in Antwerp,Belgium.Aertssen gives in his papers muchinformation and data. The following areused to compare them with the predictions:power delivered at the propeller, numberof revolutions per minute of the propeller,speed, significant wave height and thesignificant amplitudes of pitch and heavemotions and vertical bow acceleration.For m.s. Lukuga, m.s. Lubumbashi andm.s. Jordaens, the increase of power due tofouling is assumed to be 8 per cent of thepower in still water at the same speed. Incalculating the still water resistance of m.s.Dart Europe no allowance is made for thebulbous bow, so it is assumed that increaseof power due to fouling will be nullifiedby decrease of power due to a bulbousbow.In order to get a good comparison it isnecessary to use the actual torque-rpmrelation in the calculations. Figure 5 showsthese relations for the torque measured atthe propeller. Those measurements aredivided into groups having broadly thesame torque. Assuming a constant torqueat a constant engine setting, this meansgroups of a constant engine setting. For atorque equal to the torque derived from thebreak horsepower of the engine and a

maximum rpm belonging to it, the enginesetting is assumed to be 100 per cent.The comparison between predictions andmeasurements are shown in Figures 6, 7, 8and 9. The predicted speeds are inreasonably good until very goodagreement with the mean values of themeasurements. In rough seas however thepredicted speeds are a little bit too low, butthe measurement points scatter more thantwo knots. The predicted number ofrevolutions is somewhat too high; in mildweather conditions even higher than themaximum value limited by the governor ofthe engine. Figure 11 shows that this canpartly be caused by the estimated wakeand thrust deduction fraction. Anotherreason can be a possible differencebetween the characteristics of the actualpropeller and the characteristics of theWageningen B-series propeller used in thecalculations. The predicted significantamplitudes of pitch and heave motions andvertical bow accelerations are in goodagreement with the measurements byAertssen.The calculated limits of speed andsignificant wave height for voluntaryspeed reduction due to the two criteria ofOchi and Motter are also plotted in theFigures 6, 7, 8 and 9. There was no badweather in head seas during theexperiments of m.s. Lukuga in full 1oadcondition and m.s. Lubumbashi in bothloading conditions. The criteria could notbe checked in these cases.The criterion for full load condition (in theFigures marked by SH) with a maximumprobability of shipping water andexceeding g⋅4.0 by the significant ampli-tude of the bow acceleration of 7 per cent,seems to be too low for m.s. Jordaens andm.s. Dart Europe.The criterion for light load condition (inthe Figures marked by SL) with amaximum permitted probability ofslamming and exceeding g⋅4.0 by thesignificant amplitude of the bowacceleration of 3 per cent, appears also to

14

be too low. The criterion valid in full loadcondition seems to be better here. Moreinvestigations are necessary to get goodmean values for these percentages used inthe program.The predictions of this computing methodare also compared with measurements onturbine ships. In 1972 Beukelman andBuitenhek carried out experiments on thecontainership Atlantic Crown [27]. In thecalculations it is assumed that the stillwater resistance of this twin-screw shipwith a bulbous bow, including fouling, isequal to the still water resistancecalculated by the method of theShipbuilding Research Association ofJapan for single-screw ships with aconventional bow, excluding fouling. Theagreements between predictions andmeasurements of speed, number ofrevolutions and pitch and heave motionsare very good as is shown in Figure 10.The routing office of the RoyalNetherlands Meteorological Institute madespeed loss graphs available for a group ofturbine ships. For one of these ships, t.s.Kelletia, predictions are made in full loadcondition. The increase of power due tofouling is assumed to be 8 per cent of thepower in still water at the same speed. Thepredictions and observations are shown inFigure 10. Maximum observed speeds arein good agreement with the predictedspeeds at 7500 horsepower. The maximumcontinuous number of revolutions of thepropeller, 100 rpm, is in very goodagreement with the predicted value.

6 Final Remarks

The calculation of the three components ofthe total resistance and the speed of a ship,at a constant engine setting in a seaway,shows in Figure 12 for m.s. Lubumbashithat added resistance due to waves can bea considerable part of the total resistance.At a significant wave height correspondingwith Beaufort 6 the added resistance isequal to the still water resistance. Of

course this is depending on the ship’slength.In designing a ship, much attention will bepaid to the still water resistance in relationto bull form and expensive bulbous bows.On the North Atlantic however, a sea stateof Beaufort 6 is exceeded in 70 per cent ofthe time during the winter season. In thesummer season this percentage is 45 [21].Considering this, it is worth while to paymore attention to added resistance andmotions in a seaway.The program ROUTE can be an expedientfor investigating this problem. Thisprogram can be made suitable forcalculating the fuel consumption of a shipin a seaway after which it can be used forrouting a ship with a minimum use of fuel,predictions of fuel consumption, etc.Except for routing purposes, this programcan be used for the determination ofneeded machine power at a service speedin a certain state and choice of a propellerin the regular design procedure of a ship,in lengthening of ships, etc. In the nearfuture this program will also be madesuitable for following waves.

7 Acknowledgement

The author wishes to thank Prof. ir. J.Gerritsma and Mr. W. Beukelman for theirstimulating attention paid to this work andtheir valuable advises and remarks.The conversations with Ir. D. Moens of theRoyal Netherlands Meteorological Insti-tute about routing problems are very muchappreciated.Last but not least the preparation of thegraphs by Mr. P. de Heer is gratefullyacknowledged.

8 References

[1] W. D. Moens, Meteorological Route-ing (in Dutch).

15

[2] Design Charts for the PropulsivePerformances of High Speed CargoLiners, The Shipbuilding ResearchAssociation of Japan, 1964.

[3] A. J. W. Lap, Diagrams for Deter-mining the Resistance of Single ScrewShips, International Shipbuilding Progress,Vol. 1, No. 4, 1954.

[4] W.H. Auf ‘m Keller, Extended Dia-grams for Determining the Resistance andRequired Power for Single Screw Ships,International Shipbuilding Progress, Vol.20, No. 225, 1973.

[5] W. Beukelman and E.F. Bijlsma, Des-cription of a Program to Calculate theBehaviour of a Ship in a Seaway (namedTRIAL), Report 383, Delft University ofTechnology, Ship Hydromechanics Labo-ratory.

[7] J. Gerritsma and W. Beukelman,Analysis of the Modified Strip Theory forthe Calculation of Ship Motions and WaveBending Moments, Netherlands ShipResearch Centre TNO, ShipbuildingDepartment, Report 96-S.

[8] J. Gerritsma and W. Beukelman,Analysis of the Resistance Increase inWaves of a Fast Cargo Ship, InternationalShipbuilding Progress, Vol. 19, No. 217,1972.

[9] M.W.C. Oosterveld and P. van Oos-sanen, Recent Developments in MarinePropeller Hydrodynamics, InternationalJubilee Meeting 1972, NSMB, Wagen-ingen.

[10] M.W.G. Oosterveld and P. van Oos-sanen, Representation of PropellerCharacteristics Suitable for PreliminaryShip Design Studies, International Con-ference on Computer Applications in theAutomation of Shipyard Operation andShip Design, Tokyo, 1973.

[11] W. J. Luke, Experimental Investi-gation on Wake and Thrust DeductionValues, Trans. of the Inst. of Naval Arch.,1910, 1914, 1917.

[12] S.A. Harvald, Wake of MerchantShips, Doctor's Thesis, The Danish Tech-nical Press, Copenhagen, 1950.

[13] 0. Geisler and G. Siemer, DynamischeBelastung von Schiffsdampfturbinen-anlagen bei Umsteuer-Manövern, Schiffund Hafen, Heft 3, 1974.

[14] A.J.H. Goodwin, et. al., The PracticalApplication of Computers in Marine Engi-neering.

[15] Shipment of Water in Waves, TheSociety of Naval Architects of Japan, 60th

Anniversary Series, Vol. 8, Par. 6.4, 1963.

[16] M.F. van Sluys and Tan Seng Gie,Behaviour and Performance of CompactFrigates in Head Seas, InternationalShipbuilding Progress, Vol. 19, No. 210,February 1972.

[17] M.K. Ochi and E. Motter, Predictionof Extreme Ship Responses in Rough Seasof the North Atlantic, InternationalSymposium on the Dynamics of MarineVehicles and Structures in Waves.London, 1974, Paper 20.

[18] M.K. Ochi, Prediction of Occurrenceand Severity of Ship Slamming at Sea, 5th

Symposium on Naval Hydrodynamics,Bergen, Norway, 1964.

[19] G. Aertssen, Service Performance andSeakeeping Trials on m.v. Jordaens,

[20] G. Aertssen, Laboring of Ships inRough Seas, SNAME, Diamond JubileeInternational Meeting, New York, 1968.

[21] J. Gerritsma, Sustained Sea Speed,12th ITTC, Rome, 1969.

16

[22] J. Fukuda, Y. Ono and G. Ogata,Determination of Fore and After Draughtof Ballasted Bulk Carriers Associated withthe Criteria of Slamming and PropellerRacing, 11th ITTC, Tokyo, 1966.

[23] G. Aertssen, Service Performance andSeakeeping Trials on m.v. Lukuga.

[24] G. Aertssen, Sea Trials on a 9500 TonDeadweight Motor Cargo Liner.

[25] G. Aertssen, Further Sea Trials on theLubumbashi.

[26] G. Aertssen and M.F. van Sluys, Ser-vice Performance and Seakeeping Trialson a Large Containership, TRINA, Vol.114, 1972.

[27] W. Beukelman and M. Buitenhek,Full Scale Measurements and PredictedSeakeeping Performance of the Container-ship Atlantic Crown, TNO Report 185S.

[28] J.M.J. Journée, Motions, Resistanceand Propulsion of a Ship in LongitudinalRegular Waves, Report 428, Delft Univer-sity of Technology, Ship HydromechanicsLaboratory, February 1976.

9 List of Symbols

SWR still water resistance

WR wind resistance

AWR added resistance due to waves

TR total resistanceT trust of the propellerQ torque at the propeller

mQ torque at the engine

0Q torque at the engine(design maximum)

n number of revolutions0n number of revolutions

(design maximum)a coefficient for the torque-rpm

relation

P poweraV speed of advance

V ship’s speedt thrust deduction fractionw wake fraction

WV true wind speed

Wα true wind direction

3/1H significant wave heightT average wave periodµ wave directionc steam or fuel inlet ratio

mη mechanical efficiency of the shaftbearings

TK thrust coefficient

QK torque coefficientρ density of waterD diameter of propellerJ advance coefficient

Rη relative rotative efficiencyL lengthB breadthT draught

bC block coefficient

wpC water plane coefficientθ pitch motionz heave motionv absolute vertical motionv!! vertical accelerations relative vertical motion

bx longitudinal distance to centre ofgravity

aζ wave amplitude

eω frequency of encounter

..S spectral value

..m variance or spectral momentf geometric freeboard

ef effective freeboard{ }Pr probability

g acceleration of gravityω circular wave frequency

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Figure 5 Measured and Assumed Torque-RPM Relation for Diesel Propelled Ships

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Figure 6 Predicted and Measured Behaviour of m.s. Lukuga in a Seaway (Head Waves)

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Figure 7 Predicted and Measured Behaviour of m.s. Lubumbashi in a Seaway (Head Waves)

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Figure 8 Predicted and Measured Behaviour of m.s. Jordaens in a Seaway (Head Waves)

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Figure 9 Predicted and Measured Behaviour of m.s. Dart Europe in a Seaway (Head Waves)

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Figure 10 Predicted and Measured Behaviour of 2 Turbine Ships in a Seaway (Head Waves)

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Figure 11 Influence of Estimated Wake and Thrust Deduction Fraction on Calculated Speedand RPM

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Figure 12 Division of the 3 Components of Total Resistance at a Constant Engine Setting ofa Ship in a Seaway (Head Waves)