377
1 INTRODUCTION
For correct design of propulsion system with screw
propeller for inland waterway vessel the precise
determination of propeller‐hull interaction
coefficients is required. These coefficients are the
wake fraction (denoted with w) and the thrust
deduction factor (denoted with t). The former
coefficient describes the actual inflow velocity to
propeller, tha
t is usually lower than ship speed
becauseofwakebehindtheship.Thelatterdescribes
the increase in hull resistance due to the suction of
propeller, and is used to determine the thrust
requiredtoachievetheassumedshipspeed.Propeller
thrustatgivenshipspeedisusuallygreatertha
nthe
resistanceoftowedshiphull.
The proportion (1‐t)/(1‐w) in naval architecture is
called the ‘hull efficiency’. Actually, it is not the
efficiency in meaning of technology. It is rather the
coefficientthataccountsfortheinfluenceofpropeller‐
hull hydrodynamic interaction on the efficiency of
propulsion system. Hull efficiency greater tha
n 1.0
means that there is the beneficial mutual fit of
propellerandhull,andincreasestheoverallefficiency
ofpropulsionsystem.
Errors in determination of values of interaction
coefficients in the course of ship design are bad for
operation of propulsion system in real operating
condit
ions [8]. The error in determination of wake
fractionresultsinerrorsinadvancespeedV
Aandin
open water efficiency of propeller η
0. The difference
between assumed and actual value of efficiency is
determinedbythefollowingequation:
111
1
Q
o
T
oQT
K
d
K
wdw
J
wwK J K J J


 (1)
Coefficients of Propeller-hull Interaction in
Propulsion System of Inland Waterway Vessels with
Stern Tunnels
J
.Kulczyk&T.Tabaczek
WrocławUniversityofTechnology,Wrocław,Poland
ABSTRACT:Propeller‐hullinteraction coefficients‐ thewakefractionandthethrust deduction factor‐ play
significantroleindesignofpropulsion systemof aship.Inthecase ofinlandwaterwayvesselsthereliable
methodofpredictingthesecoefficientsinearlydesignstageismissing.Basedontheoutcomesfrommodeltests
andfromnumericalcomputationsthepresentaut
horsshowthatitisdifficulttodetermineuniquelythetrends
inchangeofwakefractionandthrustdeductionfactorresultingfromthechangesofhullformoroperating
conditions.
Nowadaystheresistanceandpropulsionmodeltestsofinlandwaterwayvesselsarecarriedoutrarelybeca
use
ofrelativelyhighcosts.Ontheotherhand,thedegreeofdevelopmentofcomputationalmethodsenables’to
estimatethereliablevaluesointeractioncoefficients.Thecomputationsreferredtointhepresentpaperwere
carriedoutusingtheauthors’ownsoftwareHPSDKSandthecommercia
lsoftwareAnsysFluent
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 8
Number 3
September 2014
DOI:10.12716/1001.08.03.08
378
andaffectstheshipspeed:
1
dV w dw
Vww
 (2)
where:
η
0‐openwaterefficiencyofpropeller,
J ‐advancecoefficientofpropeller,
w ‐wakefraction,
K
T‐thrustcoefficient,
K
Q‐torquecoefficient,
V ‐shipspeed.
When w<0.5 the relative error in speed dV/V is
smallerthantheerrorinwakefractiondw/w.Positive
value of dw/w results in higher actual speed. In
predictionofshipspeedtheunderestimatedvaluesof
wakefractionmaybecomebeneficial,especially
when
thehighestpossibleshipspeedisthegoalofpropeller
design.
For sea‐going ships there is a number of reliable
empiricalformulaeintheliteraturefordetermination
of values of interaction coefficients. Those formulae
arebasedontheresultsofsystematicmodeltestswith
varioushullforms.Forinland
waterwayvesselssuch
formulae are missing because of lack of systematic
model tests. The effects of water depth, ship speed
(propeller loading) and height of stern tunnel(s) on
wake fraction and thrust deduction factor have not
been sufficiently investigated. The outcomes from
tests carried out with motor cargo vessel GUSTAW
KOENIGS[1]showthattheeffectofstreaminwater
on wake fraction and thrust deduction factor is also
significant.
Available outcomes from model tests and results
ofnumericalcomputationsarenotnumerousenough
topredictthevaluesofinteractioncoefficientsreliably
inthecaseofnewly‐designedvesselsorin
thecaseof
variableoperatingconditions.
2 DETERMINATIONOFINTERACTION
COEFFICIENTS
Wake fraction and thrust deduction factor for given
ship are determined using the results of resistance
andpropulsionmodel tests,theresultsofnumerical
computations,orempiricalformulae.
Modeltestsaretimeconsumingandexpensive.In
thecaseof
inlandwaterwayvesselthecostsofmodel
tests are high in comparison to the costs of ship
design and construction. Therefore they are carried
outrarely.
Numerical computations using the commercial
CFD software provide reliable results, but are also
labourconsumingandrequiretheefficienthardware.
Computationsarealsoexpensive.
Empirical
formulae based on outcomes from
numerousmodeltestsandondatafromoperationof
real vessels, are commonly used in early design
stages, as well as in real‐time control of propulsion
system. The methods developed for sea‐going ships
arepreciseenoughowingtonumerousexperimental
data from model
tests. For inland waterway vessels
the reliable empirical formulae are missing due to
much less number of model tests carried out in the
past..
Thedeterminationofthrustdeductionfactorbased
on data from model tests or results of numerical
computations of ship flow(withoperating propeller
and without propeller) is
straightforward. Using
valuesofhullresistanceRandpropellerthrustTthe
value of thrust deduction factor is calculated
accordingtoitsdefinition:t=(T‐R)/T.
Twowakecoefficientsareusedindesignofscrew
propellers: the nominal wake fraction (in propeller
disk behind the hull towed
without propeller,
denotedwithw
n)andtheeffectivewakefraction(for
propeller operating in ship wake, denoted with w
e).
Thenominalwakefractionrepresentstheactualmean
velocity of wake flow in propeller disk V
n. It is
defined as proportion w
n=(VS‐Vn)/VS, and is
determined based on direct measurements or
computations of flow velocity. The effective wake
fraction represents the men inflow velocity to the
propeller operating in ship wake or, otherwise the
advance speed of propeller V
A. It is defined as
proportion w
e=(VS‐VA)/VS, and accounts for the
influence of the running propeller on flow in hull
boundarylayerandwake. Effective wake fraction is
determined using the magnitudes measured in
propulsion test and the open water hydrodynamic
characteristicsof propeller. Performanceofpropeller
operatinginshipwake(thrustortorque)iscompared
to
the performance of the same propeller in open
water, with assumption of thrust identity or torque
identity, in order to determine advance speed V
A.
Thrust identity is usually applied in model tests.
Torqueidentityisappliedtofullscalemeasurements
when only torque is meas ured on propeller shaft.
Values determined with the assumption of torque
identity may differ considerably from values
determined with the assumption of thrust identity.
Recommended procedures prepared by the
International
Towing Tank Conference [9]
standardize the methodology of determination of
propeller‐hullinteractioncoefficients.
In the following sections the authors present the
analysisofthe influenceofoperating conditions(i.e.
shiploading,waterdepthandshipspeed)andheight
of stern tunnelon propeller‐hull interaction
coefficientsforinlandwaterway
vessels.Theanalysis
isbasedonoutcomesfrommodeltestsandresultsof
numerical computations. It refers to conventional
inland waterway cargo ships with stern tunnels‐
motorcargovesselsandpushedbargetrainsmadeup
ofdumbbargescoupledwithapushboat.
3 INTERACTIONCOEFFICIENTSFORMOTOR
CARGOVESSELS
Mainparticulars
andhullformsofconsideredmotor
cargovesselsarepresentedinTable1andinFigures1
and2.
ModeltestsofmotorcargovesselBM‐DUISBURG
[3] included the measurements of flow velocity in
propellerdiskwithoutpropeller(nominalwake)and
themeasurementsofflowvelocityinplanelocated
in
379
distance 0.4 of propeller diameter in front of
operating propeller (Fig. 1). Effective wake fraction
was determined with assumption of thrust identity.
Testswerecarriedoutatvariousoperatingconditions
(shipdraught,waterdepthandshipspeed‐seeTable
1).
Conventionalresistanceandpropulsiontestswere
carried out with motor
cargo vessel OBM [2].
Effective wake fraction was determined with the
assumption of thrust identity as well as torque
identity, in wide range of ship speed, for the vessel
sailingalone(‘solo’)andcoupledwithasingledumb
barge (‘kombi’). Model tests of OBM in both
arrangements were also reproduced
in numerical
computations [7]. Tests and computations were
carriedoutattwovaluesofdraught,indeepandin
shallow (h/T=1,56) water. Results are presented in
Table2.
Figue1.HullformofmotorcargovesselBM‐DUISBURG
Figue2.HullformofmotorcargovesselOBM
Table1.Mainparticularsandoperatingconditionsofmodelships,[3],[2]
__________________________________________________________________________________________________
VesselBM‐DUISBURGOBM
Scale1:12.51:16
L
WL[m]6.604  6.760  6.768  6.6044.239  4.329
B[m]0.757  0.757  0.757  0.7570.558  0.558
T[m]0.200  0.224  0.256  0.2000.100  0.148
C
B[‐]0.874  0.875 0.876 0.8740.876 0.899
h[m]0.400.280.156 0.156
V
[m/s]1.336  1.267  1.171  1.1000.417  0.417
Propellers
typescrewpropellerductedpropellerKa4‐55
D[m]0.1200.0813
P/D[‐]0.650.90
A
E/AO[‐]0.560.55
__________________________________________________________________________________________________
380
Table2.Resultsofmodeltestsandnumericalcomputations
__________________________________________________________________________________________________
VesselBM‐DUISBURGOBM
Scale1:12.51:16
T[m]0.200  0.224  0.256  0.2000.100
h[m]0.400.280.156
h/T2.00 1.79 1.56 1.401.56
V[m/s]1.336  1.267  1.171 1.1000.417  0.556  0.695
Fn
h0.67 0.64 0.59 0.660.34 0.45 0.56
n[rps]26.22 26.10 26.00 25.80
Coefficientsofpropeller‐hullinteraction
Test w
n0.276  0.245 0.232 0.438‐‐‐
w
eT0.27 0.23 0.20 0.260.143  0.054  0.020
w
eQ‐‐‐‐0.685  0.2462 0.1565
w
zp0.09 0.06 0.01 0.11‐‐‐
t 0.245  0.270  0.270  0.2920.320  0.274  0.244
Comput.w
n 0.223 0.220 0.217 0.2340.335 0.332 0.312
Fluent w
e‐‐‐‐‐‐‐
w
zp‐0.383‐0.309‐0.260‐0.276‐0.304‐0.382‐0.391
t 0.267  0.243  0.262  0.2880.345  0.326  0.353
Comput.w
n 0.234 0.240 0.300 0.3220.275 0.270 0.270
HPSDKw
e0.172  0.200  0.258  0.213‐‐‐
w
zp‐0.1260.161  0.211‐0.148‐‐‐
t‐‐‐‐‐‐‐
__________________________________________________________________________________________________
w
eT
- effective wake fraction based on thrust identity
w
eQ
- effective wake fraction based on torque identity
w
zp
= (V
S
-V
zp
)/V
S
where V
zp
denotes the mean velocity in front of operating propeller, and V
S
is the corresponding ship speed
w
zp
= (V
S
-V
zp
)/V
S
where V
zp
denotes the mean velocity in front of operating propeller, and V
S
is the corresponding ship speed
OBM
-0,1
-0,05
0
0,05
0,1
0,15
0,2
0 5 10 15 20
VS [km/h]
we
T=1.60m, deep w.
T=2.36m, deep w.
T=1.60m, h=2.5m
OBM
-0,2
-0,1
0
0,1
0,2
0,3
0,4
0,5
0,6
0 5 10 15 20
VS [km/h]
t
T=1.60m, deep w.
T=2.36m, deep w.
T=1.60m, h=2.5m
Figure3.Wakefraction(we≡weT)andthrustdeductionfactor
(t)formotorcargovesselOBM(inmodelscale)
OBM : T=1.60m, deep water
-0,1
-0,05
0
0,05
0,1
0,15
0,2
0 5 10 15 20
VS [km/h]
we
'solo'
'kombi'
OBM : T=1.60m, deep water
-0,2
-0,1
0
0,1
0,2
0,3
0,4
0,5
0,6
0 5 10 15 20
VS [km/h]
t
'solo'
'kombi'
OBM : T=2.36m, deep water
-0,1
-0,05
0
0,05
0,1
0,15
0,2
0 5 10 15 20
VS [km/h]
we
'solo'
'kombi'
381
OBM : T=2.36m, deep water
-0,2
-0,1
0
0,1
0,2
0,3
0,4
0,5
0,6
0 5 10 15 20
VS [km/h]
t
'solo'
'kombi'
OBM : T=1.60m, h=2.5m
-0,1
-0,05
0
0,05
0,1
0,15
0,2
0 5 10 15 20
VS [km/h]
we
'solo'
'kombi'
OBM : T=1.60m, h=2.5m
-0,2
-0,1
0
0,1
0,2
0,3
0,4
0,5
0,6
051015
VS [km/h]
t
'solo'
'kombi'
Figure 4.Comparison ofwake fraction(we≡weT)and thrust
deduction factor (t) for motor cargo vessel OBM sailing
alone (‘solo’) and coupled with a single dumb barge
(‘kombi’)
OBM 'soko'
-0,1
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0 5 10 15 20
VS [km/h]
we
weT, T=1.60m, deep w.
weT, T=2.36m, deep w.
weT, T=1.60m, h=2.5m
weQ, T=1.60m, deep w.
weQ, T=2.36m, deep w.
weQ, T=1.60m, h=2.5m
OBM 'kombi'
-0,1
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0 5 10 15 20
VS [km/h]
we
weT, T=1.60m, deep w.
weT, T=2.36m, deep w.
weT, T=1.60m, h=2.5m
weQ, T=1.60m, deep w.
weQ, T=2.36m, deep w.
weQ, T=1.60m, h=2.5m
Figure5.Comparisonofeffectivewakefractiondetermined
with assumption of thrust identity (w
eT) and determined
with assumption of torque identity (w
eQ) for motor cargo
vesselOBMsailingalone(‘solo’)andcoupledwithasingle
dumbbarge(‘kombi’)
BM-DUISBURG
0
0,05
0,1
0,15
0,2
0,25
0,3
22,533,5
T [m]
we
BM-DUISBURG
0
0,05
0,1
0,15
0,2
0,25
0,3
22,533,5
T [m]
t
Figure6.Theeffectofshiploading(shipdraught)onwake
fraction(w
e)andthrustdeductionfactor(t)formotorcargo
vesselBM‐DUISBURGatconstantdepthofwaterh=5.0m(in
modelscale)
BM-DUISBURG
0
0,05
0,1
0,15
0,2
0,25
0,3
23456
h [m]
we
BM-DUISBURG
0
0,05
0,1
0,15
0,2
0,25
0,3
0,35
23456
h [m]
t
Figure7.Theeffectofwaterdepthonwakefraction(we)and
thrust deduction factor (t) for motor cargo vessel BM‐
DUISBURGatconstantdraughtT=2.50m(inmodelscale)
When ship speed increases the effective wake
fraction is getting weaker (Fig. 3). In deep water, at
speedshigherthan12km/hbecomesalmoststeady.In
shallowwater(h/T=1.56)thewakefractiondecreases
faster, and at speed of 12km/h (Fn
h=0.67) is
considerably less than in deep water, because of
intensive sinkage and trim by stern. The change of
draught in deep water does not affect the wake
382
fractionasfarastopofsterntunnelisbelowthefree
surface in calm water. In arrangement with dumb
barge (‘kombi’) both values and trends in change of
the effective wake fraction are almost the same as
whensailingalone(Fig.4).
When ship speed increases the thrust deduction
factor also increases (Fig. 3). In shallow water the
values are greater than in deep water. The effect of
draughtathighestspeedindeepwaterisnegligible.
BasedondatashowninFig.4onecannotconclude
the changes in thrust deduction factor caused by
enlargement of ship
length (by coupling with a
barge).
The diagrams shown in Fig. 5 illustrate the
differencebetween values of wakefraction
determined with the assumption of thrust identity
and determined with the assumption of torque
identity.
The extent of model tests with the motor cargo
vesselBM‐DUISBURGallowstoidentifythe
variation
of interaction coefficients caused by change of
draught in shallow water (1.56≤h/T≤2.00; see Fig. 6).
When ship draught increases the wake fraction
evidently decreases due to decreasing under‐keel
clearancebetweenshipand bottom of waterway. At
the same time the thrust deduction factor slightly
increases.
Reduction
ofwaterdepthatconstantshipdraught
causedtheweakeningofwakeandintensificationof
propeller suction (Fig. 7). Reduction of under‐keel
clearance is considerable and one might expect
greater difference between values of wake fraction.
However, the trends are the same as in the case of
reductionofunder
‐keel clearance by increasing ship
draught at constant water depth, or in the case of
transition from deep to shallow water in tests with
motorcargovesselOBM.
4 INTERACTIONCOEFFICIENTSFORPUSHED
BARGETRAINS
Model tests of pushed barge trains with twin‐
propeller pushboat and triple‐propeller pushboat
were
carried out in research centre in Duisburg [4],
[5]. The twin‐propeller pushboat was tested in train
with4dumbbargesarrangedintworows,at barge
draught of 2.8m (0.175m in model scale) and 3.2m
(0.200minmodelscale).Thetriple‐propellerpushboat
was tested in train with 6dumb
barges arrangedin
tworows,atbargedraughtof3.0m(0.188minmodel
scale). Numerical computations were carried out
usingtheoreticalmodel describedin[6],atthesame
operating conditions as in model tests. Main
particularsofpushboatsanddumbbargeEUROPAII
are given in Table 3. Hull
forms of considered
pushboatsareshowninFigures8and9.
Table 3. Main particulars of tested pushboats and dumb
barges[4],[5]
_______________________________________________
Vessel Twin‐ Triple‐Dumbbarge
screw screwEUROPAII
pushboat pushboat
_______________________________________________
Scale 1:16 1:161:16
L
OA[m] 2.1875 2.18754.7813
L
WL[m] 2.1188 2.1181 4.565 4.587 4.611
B[m] 0.875  0.9344 0.706 0.706 0.706
T[m] 0.1093 0.10625 0.175 0.1875 0.200
C
B[‐] 0.622  0.6426 0.947 0.946 0.945
Screwpropeller
z 44
D[m]0.13125 0.13125
P/D[‐] 1.052  1.052
A
g/A0[‐] 0.71 0.71
h[m]0.3125
_______________________________________________
Table4.Resultsofmodeltestsandnumericalcomputations
_______________________________________________
VesselTwin‐screw Triple‐screw
pushboat pushboat
_______________________________________________
h[m]0.31250.3125
T[m]0.10930.10625
(pushboat)
T
B[m](dumb 0.1750.200  0.188
barges)
h/T
B 1.79 1.56 1.67
V[m/s]0.8880.835  0.873
Fn
h0.51 0.48 0.50
n[rps]16.0716.13  15.20
Central Side Side
propellerpropeller propeller
(screw (ducted
prop.) prop.)
Modeltestw
n 0.4380.471 0.625 0.520  0.520
w
e 0.3180.324 0.39 0.46‐
w
zp 0.0720.090 0.064 ‐0.029‐0.4126
t 0.20 0.21‐‐‐
Comput. w
n 0.4090.463 0.628 0.629  0.629
(HPSDK) w
e 0.2110.244 0.657 0.543  0.543
w
zp 0.1070.113 0.253 0.125‐0.188
t 0.1110.107 0.268 0.239  0.344
K
T 0.3710.383 0.440 0.424  0.435
_______________________________________________
383
Figur8.Hullformoftwin‐screwpushboat
Figure9.Hullformoftriple‐screwpushboat
The results of model tests and numerical
computationsarepresentedinTable4.
Inthecaseoftestedpushedbargetrainsinshallow
watertheincreaseofbargedraughtatconstantwater
depthcausedincreaseofwakefraction.The trendis
oppositetothatobservedinthecase ofmotorcargo
vessels and described in the preceding section. The
reason is that the draught of pushboat remained
unchangedand,infact,itwasthechangeofhullform
and not only of ship draught. Some regularities in
variation of interaction coefficients observed in the
case of motor cargo vessel do not
refer to pushed
bargetrains.
Moreover,inthecaseofpushboatsthatoperateat
almostconstantdraught,regardlessofthedraughtof
barges, the height of tunnels is usually greater than
draught, in order to accommodate propeller of
sufficientdiameter.Thatiswhythevaluesofnominal
and effective wake fraction
are, in general, greater
thaninthecaseofmotorcargovesselswherethetop
ofsterntunnelisbelowthefreesurfaceofwater.
The effect of tunnel height on coefficients of
propeller‐hull interaction was studied theoretically
forvirtualpushboatofsimplifiedhullform[7].Main
particulars of
virtual pushboat are given in Table 5.
Thesectionalongthesterntunnelofvirtualpushboat
isshowninFig.6.Accordingtothepracticeindesign
ofinlandwaterwayvessels,thetunnelheightof1.3m
is considered the maximum applicable at ship
draughtof1.0m.
Table5.Mainparticularsofvirtualpushboat[7]
_______________________________________________
Length,L[m]20.0
Beam,B[m]9.0
Draught,T[m]1.0
Heightoftunnel,h
w[m] 1.1;1.3;1.5
Slopeoftunnel,
[deg]25
_______________________________________________
Figure 6. Section along the stern tunnel of virtual pushboat
384
Three values of tunnel height were considered
(Table 6). For each height the diameter of ducted
propeller was determined with assumption, that
nozzleisintegratedwithshiphull.Usingthetestdata
of Ka4‐70 screw series in nozzle 19A the propeller
pitchwasdesignedsoastoachievemaximum
thrust
atgivenadvancespeedV
A=2.1m/s.Thrustofpropeller
and mean pressure gradient in propeller disk were
determinedforthreeva luesof shipspeed,basedon
propulsive characteristics. The results are presented
inTable6.
Table6.Diameterandthrustofductedpropellers designed
forvirtualpushboat
_______________________________________________
hw D Z0 n VS T p
[m] [m] [m] [rps] [m/s] [kN] [kPa]
_______________________________________________
1.10.91 0.64 12.0 0.10  37  56.9
1.56 33  50.7
3.12 24  36.9
1.31.08 0.75 7.50.10 44  48.0
2.31 35  38.2
3.47 31  33.8
1.51.24 0.87 6.67 0.10 48  39.7
2.36 37  30.6
3.54 32  26.5
_______________________________________________
UsingCFDsoftwareAnsysFluentandtheactuator
diskwithpressuregradienttosimulatetheactionof
propeller a series of numerical computations were
carriedoutatwaterdepthof1.5and3.0m.Thevalues
ofnominalwakefractionandthrustdeductionfactor
determined for virtual pushboat are presented
in
Table7.
Table7. Nominalwakefractionandthrustdeductionfactor
determinedforvirtualpushboat
_______________________________________________
hw[m] VS[m/s] h/T wnt
_______________________________________________
1.13.121.50.837 0.302
3.00.679 0.285
1.33.471.50.861 0.299
3.00.752 0.320
1.53.541.50.899 0.394
3.00.733 0.403
_______________________________________________
5 CONCLUSIONS
Due to the little amount of data the conclusions are
ratherqualitativethanquantitativeandrefertomodel
scale,however,shallbevalidalsoinfullscale.
The results of model tests and numerical
computations show that operating parameters
considered in this paper, i.e. ship loading (or
corresponding
ship draught), water depth and ship
speed, affect the values of both wake fraction and
thrustdeductionfactor.
Considering inland waterway vessels with stern
tunnels that do not rise above free surface of water
(h
w<h), as motor cargo vessels with full or partial
loading,onemayexpectthat:
The increase of ship speed in deep as well as in
shallowwatercauses thedecreaseofwakefraction
andincreaseofthrustdeductionfactor.Athigher
speeds in deep water the wake fraction
becomes
steady. In shallow water the wake fraction
decreases until depth Froude number (Fn
h =
V
S/(gh)
1/2
) reaches the value of 0.65. Operation of
cargo vessels at higher speed is unprofitableand
may cause grounding due to intensive trim and
sinkageofship.
Change of ship loading (and corresponding
change of ship draught) in deep water does not
affectthepropeller‐hullinteractioncoefficients.
In
shallowwaterboththereductionofwaterdepth
as well as the increase of ship draught result in
decreaseofunder‐keel clearance and inthesame
trendsinvariationofinteractioncoefficients:when
the distance between hull and waterway bottom
(or h/T ratio) decreases, wake fraction also
decreasesand
thrustdeductionfactorincreases.
The effective wake fraction determined with
assumptionoftorqueidentitydiffers significantly
from that determined with assumption of thrust
identity.
In the case of pushed barge trains the change of
barge loading (or change of barge draught) does nor
affect the draught of pushboat, and implies the change
of hull form. Regularities in variation of interaction
coefficients observed in the case of motor cargo vessel
may not obey in the case of pushed barge trains.
The results of model tests and numerical computa-
tions also show that the height of stern tunnels affects
the flow around ship considerably, and, in conse-
quence, the value of thrust deduction factor.
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