387
1 INTRODUCTION
Trimoptimisation is one of the easiest and cheapest
methodsforshipperformanceoptimisation and fuel
consumption reduction. It does not require any hull
shape modification or engine upgrade. The
optimisation can be done by proper ballasting or
choosingofproperloadingplan.
Although trim optimisation tests are considered
less import
ant than standard power performance
modelteststheycanprovidesubstantialsavingsand
areturnoninvestmentbetweenoneandsixmonths,
depending on vessel type, operation and number of
vesselsintheseries.Theenergysavingsasaresultof
trim optimisation have been proven also by Hansen
and Freund (2010), where the influence of water
depthonpossiblegainshasalsobeendescribed.
The tri
m optimisation can be made by means of
model tests or by means of computational fluid
dynamics (CFD). Some results of possible power
gainsprovenbyCFDmethodshavebeenreportedby
HansenandHochkirch(2013)andabriefcomparison
of CFD methods with model tests at model and full
scale have been presented by Hochkirch and Mallol
(2013). These studies showed tha
t generally both
methodsagreedwellwitheachotherconcerningthe
trendsinpowerrequirementwithrespecttotrim.
FORCETechnologyis aleadingconsultantinthe
tri
m optimisation, where trim tests have been
performed for almost 300 vessels including tankers,
containervessels,LNGcarriers,Ro‐Rovessels,ferries
with the majority being however container vessels.
Testingmadesofarshowspossiblefuelsavingsofup
to15%atspecificconditionscomparedtoevenkeel.
In overall fleet operations, typi
cal savings can be as
highas2to3%.
Extensive R&D campaign has been made at
FORCETechnologytounderstandthephysicaleffects
thatreducethepropulsivepower.LembLarsenetal.
(2012) presented a comprehensive analysis of
resistance and propulsive origin factors and their
influence on power requirement. It has been
concludedtha
tthepowergainismainlyofresistance
Trim Optimisation - Theory and Practice
M.Reichel,A.Minchev&N.L.Larsen
FORCETechnology,Kgs.Lyngby,Denmark
ABSTRACT: Force Technology has been working intensively with trim optimisation tests for almost last 10
years.Focushas primarilybeenputonthepossiblepower savingsandexhaustgases reduction. Thispaper
describesthetrimoptimisationprocessforalargecargovessel.Thephysicsbehindchangedpropulsivepower
isdescribedandtheanalysesinordertoelab
oratetheoptimumtrimmedconditionsarepresented.Different
methods for prediction of required power in trimmed conditions are presented and results are compared
againsteachother.Themethodswiththeiradvantagesanddisadvantagesarediscussed.Onthebasisofpower
prediction,atri
mguidancewithdedicatedSeaTrim®softwareforshipmasterismadeandpresented.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 8
Number 3
September 2014
DOI:10.12716/1001.08.03.09
388
origin,butchangesinthepropulsive coefficientsare
alsoapartofperformancechange.
ThetrimoptimisationguidelinesmadebyFORCE
Technologyandproceduredescribedinthispaperdo
not take into account operational constraints which
havetobeconsideredduringshipping,i.e.slamming
andgreenwaterondeck,crew
comfortzone,strength
andstability,manoeuvrabilityandoverallsafety.
2 TRIMOPTIMISATIONINTHEORY
Trimisdefinedasthedifferencebetweenthedraught
atAP
A
T andthedraughtatFP
F
T .
AF
Trim T T (1)
Thisresultsinpositivetrimtotheaft.Furthermore
when a vessel is trimmed, the displacement and
speed are kept constant, i.e. no extra ballast added
andthepowerconsumptionvariesiftheresistanceis
changedwhentrimmed.
Thetrimoptimisationobjectiveistominimisethe
required power at
vessel specific displacement and
specific speed. The physical effects that reduce the
propulsivepower
D
P whenashipistrimmedcan
relate primarily to the hull resistance
T
R
and to
thetotalpropulsive efficiency
D
asshowninthe
formulabelow:
T
D
D
RV
P
η
(2)
The ship speed
V is from definition kept
constant,soitisobviousthattheaimistoreducethe
resistanceand/orincreasethetotalefficiencyinorder
togainfromtrimming.
2.1 Resistancereduction
The still water ship resistance is, according to ITTC
standards,describedbythefollowingformula:
2
TT
R½ρVSC (3)
Changes in vessel resistance can be therefore a
function of the wetted surface area
S and/or the
totalresistancecoefficient(
T
C ),andbothparameters
havetobereducedinordertogainfromthetrim.
Thewettedsurfaceareaiscalculatedforthevessel
at rest, i.e. without dynamic sinkage and trim. The
variationinwettedsurfaceareaduetotrimrelatesin
mostcasestothelargeflatsternarea
andisrelatively
small.Itcanreachupto±0.5%oftheevenkeelwetted
surface and therefore the total resistance varies the
sameduetolinearproportionality.
Thereductionofthetotalresistancecoefficient,see
eq. (4) below, can be achieved by reducing all its
components.
TR F0A
CC 1kC C
(4)
The allowance coefficient
A
C
is normally
however kept constant unless for vessels with large
variation in the draught, e.g. a VLCC in
loaded/unloadedcondition.
The frictional resistance coefficient (
0F
C ) varies,
according tothe ITTC standards, with the Reynolds
number(Re)fortheflowalongthehull:
F0
2
10
0.075
C
log Re 2
(5)
whereReistheReynoldsnumberdefinedby:
wl
VL
Re
(6)
From (5) and (6) it can be derived that the
frictional resistance coefficient is a function of the
water line length (
wl
L ), and that they are inversely
proportional.
Althoughthewaterlinelength inmostcasescan
vary ±5% from the even keel condition, the inverse
proportionalityresultsinanincrease/decreasein the
propulsivepowerofonly±0.5%.Theeffectcompared
totheoverallpossiblesavingsisminimal.
Theformfactor(1+k)
isoftenkeptconstantateach
draught in order to optimise the cost of the
experimental progra m in the towing tank. So in
practice this factor does not influence on the
resistance changes for different trimmed conditions.
Thisassumption,willbeinvestigatedinthepresented
case study below, where the
form factor has been
calculatedseparatelyforeachtrimmedcondition.
The residual resistance coefficient (
R
C ) is often
claimed to be the parameter most affected by trim.
Frompreviouslyanalysedcasesitcanbeseenthatthe
residual resistance coefficient at trimmed conditions
mayvaryupto±150%from theevenkeelcondition
values. That can reflect in changes of power
requirementupto±20%.
It
canbethenconcludedthatthemajorpartofthe
reduction in propulsive power, from resistance
reductionpointofview,iscausedbychangesinthe
residualresistancecoefficient.
2.2 Increaseoftotalpropulsiveefficiency
The propulsive efficiency is a product of the hull
efficiency
H
η , the open water propeller efficiency
O
η andtherelativerotativeefficiency
rr
η .
THOrr
ηηηη
(7)
None of these three contributions are necessarily
constantwhenthevesselistrimmed.
The hull efficiency is a function of the thrust
deduction
t andtheeffectivewakefraction
.w
389
1
1
H
t
w
(8)
So it is obvious that the thrust deduction should
decrease and the effective wake fraction increase in
ordertogainfromtrimming.Thethrustdeductionis
a function of the propeller thrust
T and the hull
resistance.
T
TR
t
T
(9)
As mentioned before the hull resistance changes
when the vessel is trimmed and naturally, the
propellerthrustwillchangealsoasthespeediskept
constant.However,therelationisnotconstant.
The thrust deduction changes with the trim and
sometimes a peak, when the propeller submergence
decreases to
a critical level, can be observed. The
location of the peak depends also on the dynamic
sinkageandsternwave.
The changes in thrust deduction can achieve
values of up to 15% and can result in significant
changes in the propulsive power of up to 3%.
However, changes in the thrust
deduction must be
seenrelativetochangesintheeffectivewake.
The effective wake fraction is a function of the
vesselspeedandthepropellerinflowvelocity
A
V .
A
VV
w
V
(10)
Asthevesselspeediskeptconstant,changesinthe
effectivewakefractioncanonlyrelatetothepropeller
inflow velocity. As expected, the effective wake
fraction increases for bow trim conditions and
decreases for stern trim conditions. The increase of
wakefractionforbowtrimscanbeup
to20%andthe
decrease for stern trims can be up to 10%. The
differencesinwakefractioncanthereforechangethe
powerdemandofupto5%.
Both thrust deduction fraction and wake fraction
for bow trim balance each other and can result in a
powergainupto2%.
The propeller open water efficiency depends on
the advance ratio
J
, i.e on the water inflow
velocity to propeller
A
V and on the revolutions
n :
A
V
J
nD
(11)
where
D isthepropellerdiameter.
Asalreadyconcludedthepropellerinflowvelocity
isaffectedbythetrim.Sincetheopenwatercurvefor
the propeller efficiency is inclined for the actual
advance ratio, even minor changes in the advance
ratio result in a changed propulsive power. These
changes can reach up
to 2% of the even keel power
demand.
The relative rotative efficiency is defined as the
ratio between the open water propeller torque
coefficient
ow
KQ and the propeller torque
coefficientbehindtheship
ship
KQ .
ow
rr
s
hip
KQ
KQ
(12)
Itcanvaryupto2%fromevenkeelconditionand
thesamewayinfluencethepowerrequirement.
2.3 Totalpowergain
From the theory and percentage values presented
above can be concluded that the residual resistance
coefficient is the factor most affected by trim.
However,thepropulsionaffects
theresultsata level
detectableinmodeltestsandshouldnotbeneglected.
3 TRIMOPTIMISATIONINPRACTICE
Taking into account the theory presented above,
several methods for determining the optimum trim,
whicharebasedondifferentpracticalapproachmay
be used during optimisation process. The
experimentalmethodsingeneral
canbedividedinto
threeoptions:
3.1 Fullresistanceandself‐propulsionmodeltests
Modeltestsperformedinthismethod consistoffull
set of resistance and self‐propulsion model tests for
eachtrimmedcondition.
Each condition is treated as an independent
propulsionpredictioncase,i.e.predictiontofullscale
is made according to FORCE’s procedure. This
approach fully accounts forvariation of form factor,
residual resistance coefficient and propulsive factors
(effectivewake,thrustdeductionandrelativerotative
efficiency)withdisplacement/trimvariation.Practical
drawback is the relative high experimental matrix
withassociatedincreasedcost.
3.2 Self‐propulsionmodeltestswithconstant
formfactor
andconstantthrustdeductionfraction
Inthismethodtheresistancetestsareperformedfor
reference conditions only, which in 90% of cases
means the even keel condition for each tested
displacement. Form factor and thrust deduction
fractionaretakenfromthereferencecaseandarekept
constant during
trimmed conditions analyses. The
self‐propulsion tests performed for trimmed
conditions are the basis for calculation of wake
fraction and propulsive coefficients on a basis of
reverse approach. Advantages of this approach is
somewhat reduced experimental cost, but with the
disadvantageoflosingthetrimeffectonformfactor
andthrust
deduction.
390
3.3 Directpowermeasurements
The prognosis to full scale is made on the basis of
torque and revolutions measured during the self‐
propulsion tests at ship self‐propulsion point, i.e.
including the additional towing force for
compensation of frictional resistance between ship
andmodel.Thefullscaleprognosisismade
according
to Froude similarity law. This is the most
straightforward approach, simulating the full scale
ship trial procedure. There is no need of resistance,
form factor, propeller open water data, neither
propulsive factors measurement. In this approach,
however, the effective wake scaling is neglected,
which would influence propeller loading coefficient
and subsequently propeller thrust, torque and shaft
powerprediction.
4 CASESTUDYPRESENTATION
Below the results of trim optimisation for a large
cargo ship are presented. All three methods were
usedandresultsofallmethodsarepresented. Some
detailedanalysis of form factor, residuary resistance
coefficient, wake fraction, thrust deduction
fraction,
relativerotativeandopenwaterefficienciesismade.
Resultsoftrimoptimisationarepresentedintwo‐
ways,asamatrixofpossiblepowersavingsattested
trimmed conditions and as an optimum trim at
specificdisplacement.
4.1 Referencevessel
The vessel chosen for thisstudy is a large container
vessel. The hull form represents a typical container
vesselwithapronouncedbulbousbow,slenderhull
andacentreskegwithonepropeller.
Table1.Mainparticularsofreferencevessel
_______________________________________________
Ship Model
_______________________________________________
Length,LPP330.00 8.648
Breadth,B42.80 1.122
Maxdraught(tested),T
max 11.50 0.301
Volumeatmaxdraught,V
max 104166 1.875
Blockcoefficientatmaxdraught,CB
max 0.654 0.654
_______________________________________________
Thevesselwaschosenduetoitswell‐documented
resistanceandself‐propulsionperformancebyseveral
modeltestsatFORCETechnology.Earlierithasbeen
testedinnumerouscombinationsofdraughts,speeds
and trims. In this study, only one partly loaded
draught and speeds corresponding to a Froude
number
between 0.128 and 0.201 is described. Ten
differenttrimshavebeeninvestigatedrangingfrom‐
2.5mto2.0minstepsof0.5m.
4.2 Modeltestsresults
Figures 1‐3 present the detailed comparison ofform
factor, thrust deduction and wake fraction between
two methods, i.e full resistance and self‐propulsion
model tests
for all trimmed conditions [act ff act t]
and self‐propulsion model tests with constant form
factor and constant thrust deduction fraction with
resistance tests only at reference draught [const ff
constt].
Figure 1 presents markers representing thrust
deductionfractioninmethodwithfullresistance,self‐
propulsiontestsand
asolidline,whichrepresentsthe
constant thrust deduction fraction in function of
vessel speed from method with resistance tests only
forreferencetrim.
Figure1.Thrustdeductionfractionindifferentmethods
Itcanbeseenthatthethrustdeductionfractionfor
all tested trim conditions decreases with speed and
has rather large scatter. Furthermore, there is a
pronounced trim influence with deviations (relative
totheconstanttvalue)ofupto100%.
Figure2showstherelationbetween form factors
measured at
different trimmed conditions and
constant form factor taken into account in method
with resistance testsmade only at reference trim. In
that figure also the thrust deduction fraction from
bothmethodsfordesignspeedisshown
Figure2.Formfactorusedindifferentmethods
It is clearly visible that the form factor increases
withthetrim,i.e.withmoresubmergedaftpart.The
deviationvariesbetween1.13and1.21.Howevernot
largeitisstillinfluentialonthefinalpowerprediction
becausetheymayleadtoeffectivepowervariationsin
therangeo6‐7%.
Figure 3 presents the propeller open water
efficiency derived from analysed methods. The
efficiency is presented as a relation between
calculated from full resistance and self‐propulsion
tests at each trimmed condition and calculated from
constantthrustdeductionmethod.
391
Figure 3. Relation of propeller efficiency from different
methods
The propeller efficiency received from analysed
methodscanbeingeneral treatedascomparable,the
maximum difference received is about 1.6% for the
trimtoaftanddecreaseswithtrimmingtobow.
Figure4presentstheoptimumtrimreceivedfrom
differentmethodsinfunctionofspeed.
Figure4.Optimumtrimfromdifferentmethods
Figure 4 shows that all three methods follow
similartrendregardingthevesselspeedandshowthe
optimumtrimreduceswithincreasedspeed.Itcanbe
seenhoweverthattheoptimumtrimforanyspecific
speedmay differ, e.g. for 18 knots was found‐1.7m
for the constant form factor and
constant thrust
deduction fraction and‐1.6m for actual form factor
andactualthrustdeductionfraction,whilefordirect
powermethodtheoptimumtrimisabout‐1.5m.
Figure 5 presents the overall comparison of
predicted power savings received from three
analysedmethods.
Figure5.Predictedpowersavingsfromdifferentmethods
Likeincaseofoptimumtrim,thetrendofpossible
power savings received from analysed methods is
very similar. The difference in values of predicted
possible power savings between the highest and
lowest possible saving received from different
methodsisalmostconstantandequaltoabout2.7%.
5 CONCLUSIONSONTHE
OPTIMISATION
METHODS
The final conclusions may be presented in two
aspects, i.e. showing the effect of the investigated
analysismethodonthedeterminationoftheoptimum
trim condition and showing the effect of the
investigated analysis method on the possible power
savings.
If taking into account the first aspect it
appears
that in the low to medium speed range (14 to 18
knots) the methods with full resistance and self‐
propulsion tests (act ff act t) and the one with
resistance for a reference trim only (const ff const t)
givesimilarresults (seeFigure4).Forthetop speed
range,
however,theactffactt method is preferable
foritsbetteraccountofthethrustdeductionand1+k
deviationwithspeed(seeFigure1).Thedirectpower
method follows the same trend as the indirect
methods giving however the values of trim with a
smalloffset.
Regardingthepossible
powersavingsitshouldbe
concludedthatforthemediumspeedrange(16to18
knots) the two methods, i.e. act ff act t and const ff
consttindicatesimilarpower savings, while for the
lowandtopspeedrangesdeviationsreachupto2%.
Thus, again, the actual t
and (1+k) method could be
recommended for better power saving prediction in
the entire speed range. In the direct power method,
thepredictedpowerlevelsdonotconsiderwakescale
effectandcorrelationallowancecoefficient.Therefore,
thepredictedpowersavingsaregenerallylower,but
exhibitthesametrendasthe
twoothermethods.
A general comment may be concluded that the
choice on which method to use is a compromise
between possible resources both in time, in facilities
utilisation or in software, when numerical methods
insteadofmodeltests willbe used, anda satisfying
levelofaccuracy.Howeverallthree
methodscouldbe
used to predict certain power savings coming from
trimoptimisation.
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6 SEATRIM®SOFTWARE
Force Technology has elaborated a decision support
tool, which is designed to provide a quick and safe
guidance in selection of the right trim in relation to
theloadingconditionandplannedspeed.
Only three parameters are necessary to evaluate
the influence of actual trim of the
vessel and make
optimum trim suggestions. These parameters are:
Draught forward and aft (typically taken from ship
loading computer) and the planned vessel speed
(fromvesselrouteplanning).The program will then
advisetheuseraboutthetrimsituationandwill,by
simplecolourcodesandreduction/increaseinpower,
advisetheuserifthetrimisoptimal.Shouldthetrim
notbeoptimal,thetoolgivesquickguidancetowhere
theoptimumtrimcanbefound.Theusercanthenuse
hiscargoorballast watertoobtainthebestpossible
trimbeforeleavingtheport.
Figure6.SeaTrim®software
ACKNOWLEDGEMENTS
Research presented in this paper was sponsored by
The Danish Maritime Foundation through Danish
CentreforMaritimeTechnology(DCMT)andFORCE
Technologyfrombasicresearchfund.
REFERENCES
[1]LembLarsenN., SimonsenC.D.,Klimt NielsenC.,Råe
Holm C. (2012), Understanding the physics of trim, 9
th
annualGreenShipTechnologyConference,Copenhagen,
Denmark
[2]Hansen H., Freund M. (2010), Assistance Tools for
Operational Fuel Efficiency, 9
th
International Conference
on Computer and IT Applications in the Maritime
Industries,COMPIT2010,Gubio,Italy
[3]Hansen H., Hochkirch K. (2013), Lean ECO‐Assistant
Production for Trim Optimisation, 11
th
International
Conference on Computer and IT Applications in the
MaritimeIndustries,COMPIT2013,Cortona,Italy
[4]HochkirchK.,MallolB.(2013),OntheImportanceofFull‐
Scale CFD Simulations for Ships, 11
th
International
Conference on Computer and IT Applications in the
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