505
1
INTRODUCTION
In this paper the dynamic contact forces, generated
between a “Hiload DP1” prototype attachment
system[4],[7]andthebottomofthetankerhullatthe
openseawithwaves,swelland/orcurrentwhenthe
shipsarefreelymovedinallsixaxiswithpitch,roll,
heave,surge,swayandtheyow(seefigure1),willbe
depicted. In order to discuss the dynamic contact
forcesoneneedstopreparesomecalculationsforthe
different wave headings, distributed from 0° (head
sea)to180°(followingsea).Itisessentialtoremember
that the forward transit speed of the tanker with
a
“HiloadDP1”unitdockedalongsideisassumedtobe
4knots(STW),withthetransferfunctionsandphase
angles included; the largest amplitude value in a
roughseaattheopenoceanshouldbeexpected.
Inthisstudy“HiloadDP1”prototypeunitwiththe
following ships particulars [5] will be
used: Cyprus
flagvessel,DNV1A1RMobileOffshoreSupportUnit
DYNPOS – AUTR, DP class 2 ship build in 2010,
IMO= 8770950, call sign: 5BML2, Gross Tonnage
(GRT)=1697GRT, Net tonnage(NRT)= 510, L.O.A.=
28.0 m, Breath= 27.0 m, Height from keel to top of
mast= 58.5 m,
Max operation draught= 42.0 m
(Displacement(DWT)=5544MT),Minimumdraught=
16.5m(DWT=4242MT),3xcaterpillarmainengines
each3150BHP,3 x550kWGenerators+1x315kW
Emergency Generator, 3 off Azimuth Thrusters
(WartsilaLips)directlyshaftedtoDieselCombustion
EnginesandMT
“NavionAnglia”withthefollowing
ships particulars [5]: Bahamas flag ship, DNV +1A1
Tankerforoil, Dynpos‐AUTR,DPclass 2 ship build
in 1999,IMO 9204752, call sign: C6XC8, Gross
Tonnage (GRT): 72.449, L.O.A.= 264.68 m,Breath =
42.50 m, Height from keel to top of mast= 50,0 m,
maximumdraught=15,65m,DWT=152.809MT,2x
B&Wmainengines10010kW(13420HP)each,Two
Ulsteincontrollablepitchpropeller4bladeseach,2x
bowthrustersBrunvoll2200kW(2950HP)eachand2
xsternthrustersBrunvoll735kW(990HP)each.
Numerical Analysis for the D
y
namic Forces and
Operational Risk Accomplished for a “Hiload DP1”
Unit Docked to MT “Navion Anglia” at Sea Waves
G.Rutkowski
GdyniaMaritimeUniversity,Gdynia,Poland
ABSTRACT: In this paper author depicts the results of the sea trials ofthe operational test of a Hiload
technologyatseawaveswiththenumericalanalysisforthedynamicforcesandoperationalrisk.Theresearch
wascarriedoutonboardMT“NavionAnglia”whichwasengagedinatowingoperation
throughtheAtlantic
Oceanwitha“HiloadDP1”prototypeunitdockedonherportsidealongside,withdifferentship’sdraftandin
different weather conditions. Additionally in this paper author presents the methodsthat can be used for
estimating the safety factor SF against sliding and/or operational risk for the towing
and/or manoeuvring
operationwitha“HiloadDP1”unitdockedalongsideattheopensea.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 8
Number 4
December 2014
DOI:10.12716/1001.08.04.04
506
Figure1.Functionofthe“HiloadDP1”frictionattachmentsystemafterdockingtothetankeratthecalmsea(figureonthe
left)andontheroughsea(figureontheright)withpitch, roll,heave,surge,swayandtheyowasaneffectofwindwaves,
swelland/orseacurrent.
In this paper the results of the sea trials,
accomplished at the operational tests, will be
depicted. The tests were carried out in Q3 2013 on
board MT“Navion Anglia” during her towing
operation from Norway to Brazil through the big
Atlantic Ocean with a “Hiload DP1” prototype unit
docked on her
portside alongside near amidships,
with different ship’s draft and different weather
conditions.Additionally,wealsoaregoingtodepict
the real life operational tests results carried out
offshore Brazil in 2014 on Campos Basin and/or
EspiritoSantoBasinBrazil.
We will try to present the methods that can be
used
for estimating the operational risk for towing
and/ormanoeuvringoperation with a “Hiload DP1”
unit docked alongside to the vessel at the open sea
using the definition of a safety factor (SF) against
sliding.
2
NUMERICALANALYSISOFACONTACT
FORCEGENERATEDONA“HILOADDP1”
ATTACHMENTSYSTEM
In the calm water case (see on figure 1 on the left),
Hiload DP is subjected to gravity and buoyancy
forces in the vertical direction. The connection force
betweenHiloadDPandthetankerbottomisgivenby
the difference between the buoyancy force and the
gravityforce.Itisalsoknownthatthebuoyancyforce
of a floating body equals
ρgV, where ρ is the mass
densityofwaterand
Visthesubmergedvolume.This
expression can be found by integrating the
hydrostatic pressure over the submerged surface of
the body. The same formula can be applied to
“Hiload DP1” unit docked to MT “Navion Anglia”
[4], [1]. In applying this formula we have implicitly
assumedthat the hydrostaticpressurealso
actsover
thecontactarea,
A0.Inrealitythepressureiszeroon
A0 (atmospheric pressure is treated as zero in this
analysis,sinceitactsasanadditionalpressureonall
surfaces).Hence,weneedtosubtractthehydrostatic
force on
A0, which has been incorrectly included. If
we denote forces acting upwards as positive, this
force equals‐
ρgTA0. In such cases, taking into
considerationallabove,thecorrectedbuoyancyforce
Fbcannowbewrittenasformula(1):
sbgrav 0
FFF gV gTA mg
 (1)
where:
Fs = the staticcontactforce generated on Hiload DP
attachmentsystem,[N],
Fb=theforceofbuoyancy,[N],
Fgrav=thegravityforce(theweightof“HiloadDP1”
unit),[N],
ρ=themassdensityofwater(forseawaterρ=1025
kg/m3),[kg/m
3
],
g = the acceleration due to gravity (the gravity of
Earthg=9.81m/s
2
),[m/s
2
],
V = the volume of theobject inserted into the fluid,
[m
3
],
T=thedraftofthevessel(theheight)atwhichforce
actson,[m],
A0=contactareainmetersquarewithnilhydrostatic
pressure(for“HiloadDP1”unitA
0=360m
2
estimated
fromdrawings[5]),[m
2
].
m=themassofobjectinkg,inouranalysesthetotal
massof“HiloadDP1”unitequals4674000kg,[kg]
From equation (1) it is seen that the static
connection force can be increased by reducing the
massof“HiloadDP1”unit,increasingthesubmerged
volumeof“HiloadDP1”ship,
increasingthecontact
areaorbyincreasingthedraftofthetanker.However
so far the sea waves, swell and all other dynamical
forceswerenotconsideredinthisanalysis.
In the real life operation when the tanker with a
“HiloadDP1”unitdockedalongsideistravellingina
seaway,
theyarebothsubjectedtothewaveinduced
forces,speedinduceddragandinertiaforces.Vertical
dragforceson“HiloadDP1”unitareassumedtobe
smallcomparedtothepressureforcesandtheinertia
forces in the present study. In such cases for our
simplified calculation the dynamic vertical contact
forcecanbewrittenasformula(2):
507
dd z
FpAma
(2)
where:
d
F
=thedynamicverticalcontactforce,[N],
d
p
= the hydrodynamic pressure acting on the
horizontalbottomon“HiloadDP1”unit[Pa],
A = area in meter square on horizontal bottom (on
“HiloadDP1”unitA=729m
2
asestimatedvaluefrom
drawings[5]:A=27mx27m=729m
2
)[m
2
],
m=thetotalmassofobject,for“HiloadDP1”unitm=
4674000kg,[kg]
z
a
= the vertical acceleration of “Hiload DP1” unit
[m/s
2
].
In practice, the dynamic pressure will not be
uniformoverthebottom(
A),howeverinthisproject
for our simplified analysis we can use the average
value for such pressure checked at few different
locationsatthe bottom of a “HiloadDP1” unit. The
dynamic pressure
pd and the vertical acceleration az
can be calculated with a ship motion analysis
program using the linear strip theory module i.e. in
VERESprogram[3],[1].
For “Hiload DP1” unit, the contact area with
atmosphericpressure (
A0), does not cover the entire
horizontalsurfaceatthis“deck”level.Hence,apart
ofthis“deck”levelis exposed to the hydrodynamic
pressureandthisshouldbeaccountedforinequation
(2). If the area of this part is denoted
At and the
averagedynamicpressureonthispartisdenoted
pdt
,a modified version of equation (2) becomes the
followingformula(3):
dd dtt z
FpApAma
(3)
where:
t
A
= area in meter square on horizontal bottom A
exposed to hydrodynamic pressure around contact
area. For our calculation for “Hiload DP1” unit At=
329m2astheestimatedareafromdrawings[5],[m2],
dt
p
=thedynamic(hydrodynamic)pressureactingon
thehorizontalbottompartA
t,[Pa].
In the present analysis, the pressure pdt will be
takenasthepressureunderneaththetankerbottomin
the area close to Hiload DP attachment system. For
ouranalysisthe average value of the hydrodynamic
pressure will be depicted at 4 different locations
immediatelyforwardandaftof“HiloadDP1”
unit.In
reality, there will probably be significant pressure
variationsinthenarrowgapbetweenHiloadDPand
thetankerbottomandthepressureinthisgapisalso
expectedtobequitedifferentfromthepressureonthe
partof“HiloadDP1”unitthatextendsoutsidethe
tankerhull
(thepartaroundthebaseof the towers).
An accurate assessment of the dynamic pressure p
dt
distributionoverA
tareawerethereforethepartofthe
detailed analyses carried out by Marintek company
[1]withVERESShipmotionanalysisprogram[2].
In such cases, the linear frequency‐domain strip
theory module from theVERES program [3] will be
used for further analyses, and the final results
described on Marintek
VERES simulator program
research work [1] will be used for the simplified
calculation.Finallytakingintoconsiderationthefact
that in the study mentioned above [1] it was also
noted that the correction introduced in equation (3)
doesnotinfluencetheresultssignificantlyandforour
simplifiedcalculationwecanuse
theresultobtained
directly from equation (2) without any additional
correction.
3
RESULTSOBTAINEDINVERESPROGRAM
FROMALINEARSTRIPTHEORYMODULE
ThelinearstriptheorymoduleinVERESprogramis
well suited for the analysisof the tanker motions at
different forward speed. In a linear analysis it is
implicitly assumed that there is a linear relation
between the amplitude of all response quantities
(motions,pressures,waveinducedforcesetc.)andthe
amplitude of the incidental waves which for ships
withverticalsidesinthewaterlineareaisgenerallya
valid assumption. In a linear frequency‐domain
analysis,theresponseoftheshipinregularsinusoidal
waves is calculated. This is
repeated for a relevant
range of wave frequencies, and the process is
repeatedforeachrelevantwaveheading.Thisresults
in a set of
transfer functions (RAO), which relates the
amplitude of each response to the amplitude of the
incidentwavesandthephaseoftheresponserelative
to the waves is also calculated. The responses of
interestin thepresent study are thetanker motions,
the vertical acceleration of “Hiload DP1” unit, the
dynamicpressureson“Hiload
DP1”andtherelative
waveelevationatthelocationof“HiloadDP1”.
With reference to “Hiload DP1” unit the
frame/truss structure underneath of “Hiload DP1”
unitwasnotincludedinthis analysis. Itis assumed
thatthehydrodynamicpressureunderneaththebox‐
shaped part of Hiload DP gives rise to
the most
importantverticalhydrodynamicforce.Hence,forthe
purposeofsuchcalculatingthetanker/Hiloadvertical
motion and the dynamic pressure underneath
“HiloadDP1”unit,“HiloadDP1”ismodeledasabox
underneaththetankerbottom.SinceVERESrequires
port‐starboardsymmetry, thebox extends from port
tostarboardside.In
theship’slongitudinaldirection,
thebox‐lengthis27m.
When the relevant transfer functions have been
calculated, they can be combined with a wave
spectrumtoestablishtheresponsespectrumandthe
standarddeviation.Thewavespectrumisdefinedby
thesignificantwaveheight,
Hs,andthepeakperiod,
Tp,ofthewaves.
An irregular sea state may be characterized by a
standard wave spectrum such as the Pierson–Moskowitz,
the JONSWAP (Joint North Sea Wave Project) wave
spectrum or the two peaked Torsethaugen wave spectrum
which are all available in the VERES Postprocessor [3].
The wave spectrum expresses the distribution of wave
energy (which is proportional to the wave amplitude
squared) for different wave frequencies. The standard
spectra are suitable for different types of irregular sea [3]
and different ocean areas:
The JONSWAP spectrum is assumed to be
especially suitable for the North Sea, and does not
representa fully developed sea. It has a peakedness
parameterγ, which determines the concentration of
thespectrumaboutthepeakfrequencyandusuallyis
setto3.3.
508
ThePierson–Moskowitzspectrumissuitablefora
fullydevelopedsea,i.e.aseastate
where the wind has
been blowing long enough over a sufficiently open stretch
of water, so that the high frequency waves have reached
equilibrium. At this point, the waves are breaking
slightly. In the part of the spectrum where the frequency
is greater than the peak frequency (
ω>ωp), the energy
distribution is proportional with
ω -5. For a given
significant wave height and peak period, the Pierson–
Moskowitz spectrum is identical with the Bretschneider,
ISSC and ITTC spectrum models. The Pierson–Moskowitz
spectrum appears for
γ = 1 in the JONSWAP
formulation.
The Torsethaugen spectrum is a two peaked
spectrum which includes both wind generated sea
and swell. An option is included to enable long
crested swell from a direction different from the
principal wave direction (direction of the wind
generatedwaves).
According DNV Classification Notes 30.5, the
spectral density function
for the JONSWAP (Joint
NorthSeaWaveProject)spectrumcanbewrittenas:
2
4
1
0p
p
2
p
0
5
4
25 e
00
S( ) g e











(4)
wherethewavespectrumparametersare:
α
= Spectral parameter (generalized Phillips’
constant),
g=accelerationofgravity,g=9.81m/s
2
,
ω
0=Wavefrequency[rad/sec],
ω
p=Peakfrequency,ωp=2π/Tp,
γ=Peakednessparameter,
σ=Spectralwidthparameter,σ=0.07forω0<ω
pand
σ=0.09forω
0
>ωp
ThePierson–Moskowitzspectrumappearsfor
γ
=1.Thespectralparameter α iscomputedas:

24
2
sp
s
24
p
H
H
5
1 0.287 ln 5.061 (1 0.287 ln )
16 g T


(5)
where
Hs is the significant wave height. A standard
value of the peakedness parameter
γ is 3.3.
However, a more correct approach is to relate the
peakednessparametertothesignificantwaveheight
andthepeakperiod:
ps
ps
5.75 1.15T / H
ps
ps
5forT/H3.6
e for 3.6 T / H 5
1forT/H5

(6)
IntheVERESPostprocessor,youcanchooseeither
tospecifythepeakednessparameterγdirectly,orthe
γ value can be calculated from (6) based on the
significantwaveheightandpeakperiod.
Inalinearanalysis,theprobabilitydistributionof
the response amplitudes in a given storm will be
given
by the Rayleigh distribution. The Rayleigh
distribution is defined by the standard deviation of
the response, and for a given peak period, the
standarddeviationisproportionalwiththesignificant
wave height. Hence, it is sufficient to calculate the
standard deviation for
Hs=1 for all relevant peak
periods and wave directions in order to derive
extremevaluesforhighersea‐states.
In our simplified calculations for the irregular
waves, a JONSWAP wave spectrum with peakness
parameterγ= 3.3 was used. The forces on the ship
have been found by integration of the pressure
distribution on the submerged hull. The bilge keels
wereincludedintheVERESmodel.Forrollmotions,
viscous damping forces due to bilge keels and skin
frictionwereincludedandthewaveamplitudeof2.5
m was used when these nonlinear damping forces
were calculated [1]. All other parameters from
formula(4)to(6)wereobtainedinVERESprogramas
average value adequate for North Sea and Atlantic
Ocean.
The results from the irregular waves were
generally presented in terms of standard deviations,
σ. The standard deviation is dependent on the
significant wave‐height, the period (in [1] the peak
periodisused)ofthewaves,andthewavedirection.
Inthepresentlinearanalysis,theresponseamplitudes
follow the Rayleigh distribution, and the standard
deviationofanyresponsewillvarylinearlywiththe
significant wave‐height. Hence, the results will be
presentedforaunit significantwave‐height.Insuch
case,theextremevalueswereestimateddirectlyfrom
the standard deviation. Some relevant relationships
were as follows: significant value of the response
amplitude=2*σ;expectedlargestresponseamplitude
in a sea‐state≈4*σ and extreme value of the
response amplitude with one percent probability of
exceedence≈5*σ(approximately).
The
horizontal wave drift force generated on a
vertical wall of “Hiload DP1” unit attached to MT
“Navion Anglia” can be also computed in VERES
programfromthefollowingequation:
kz
w
F2gSesin(t)

(7)
where:
Fw= horizontal wave drift force generated on a
verticalwallofHiloadDPunit[N],
ξ =waveamplitude[m],
ω=wavefrequency[Hz],
S =verticalarea [m
2
],.
k =wavenumber:k=2π/λ[radians/m],
z =immersion[m],
Inthisstudythehorizontalwavedriftforces(
Fw)
have been obtained using the VERES program for
“Hiload DP1” unit docked to the tanker at the
amidshipsareawith tankerdraft8m and10m and
with correction for immersion due to corresponding
amplitudes of the relative motion in regular waves
withamplitudesof2.5mand5m.For
waveamplitude
ξ= 2.5 m the horizontal wave drift forces were
consideredas5.55MNforthetankerdraftT=8mand
to5.05MNfortankerdraft10m.Forwaveamplitude
ξ= 5.0 m the horizontal wave drift forces were
estimatedaccordinglyas11.1MNforthetankerdraft
T=8mandto10.1MNfortankerdraft10m(seetable
1).
509
Table1. Estimation of the horizontal wave drift forces
obtainedinVERESprogramfor“HiloadDP1”unitdocked
to similar vessel (Vigdis Knutsen – 120000 DWT) as MT
“NavionAnglia”
_______________________________________________
TankerdraftT[m] Waveamplitude Waveamplitude
ξ=2.5mξ=5.0m
_______________________________________________
8m5.55MN11.1MN
10m5.05MN10.1MN
_______________________________________________
Thedynamicverticalcontactforceperunitwave‐
heighthasbeenobtainedinVERESprogramandthe
expectedmaximumdynamiccontactforceperunitHs
wasaccountedasaround2.4MNforheadwaves(0°
heading)andthewavepeakperiodaround5s.
4
OPERATIONALRISKANALYSISANDSAFETY
FACTORSFAGAINSTSLIDING
During the transit voyage, the “Hiload DP1” was
affected by dragforces generated by the water flow
arounditssubmergedpart.Itwasalsoaprerequisite
forthesafetransitoperationthatthefrictionforce,
Ff,
between “Hiload DP1” unit and the MT “Navion
Anglia”bottomremainslargerthanthesummarized
drag and wave induced horizontal forces,
Ft,
otherwise“HiloadDP1”unitcanstartslidingrelative
tothetankerhull.Insuchcases,withalltheabovethe
safety factor taken into consideration,
SF, against
slidingcanbeimplementedanddefinedas:
f
t
F
SF
F
(8)
where:
SF=SafetyFactoragainstsliding,
Ff = Friction force between “Hiload DP1” unit and
tankerbottom,[N]
.
Ft = Inducted horizontal forces effected on “Hiload
DP1”unit,[N].
Thefrictionforceequalsthecontactverticalforce
times multiplied by the friction coefficient,μ. The
contactverticalforceisthesumofthestaticandthe
dynamiccontactforcesasdescribeinfigure(11):
fsd
F(FF)
 (9)
where:
Fs =the static contact force generated by “Hiload
DP1”unitinNewton,[N],
Fd= the dynamic verticalcontactforce generated on
“HiloadDP1”unitspecifyinNewton,[N]
μ = the friction coefficient (in our analysis with
“HiloadDP1”unitequalsμ=0.6).

Thecriticalsituationiswhenthedynamiccontact
forceisnegative.Hence,wecanwrite:
sd
t
(F F )
SF
F
(10)
Insuch casesfora givensafetyfactor we get the
followingrequirementtothedynamiccontactforce:
t
ds
SF F
FF

(11)
When the transfer function for Fd has been
calculated, we can use formula (11) to evaluate the
maximum allowable significant wave height for a
givensafetyfactorandagivenpeakperiod.
5
DISCUSSIONOFTHERESULTSAND
SUMMARYREPORT
Thetankermt“NavionAnglia”isusedinthepresent
studywiththefollowing conditions:mediumballast
condition (T
1= 8m), full ballast condition (T2= 10m),
partly loaded (T
3=12 m) and fully loaded condition
(T
4=15m).Themainparticularsofthisshiparegiven
inTable2.
Theradiaofinertiahavebeenestimatedbasedon
theauthorexperiencefromthesimilarships.TheMT
“Navion Anglia” is equipped with 0.5 meter wide
bilgekeels,whichextendfromapproximately25%to
75%oftheship
lengthfromAP.
TherelevantpropertiesofHiloadDP usedinthe
presentanalysisareasfollow:totalmassm=4674000
kg, mass displacementρV= 4972141 kg for tanker
draftT=8m,5074259kgforT=10mand5176376kg
forT=12m, contact area
A0= 360 m
2
(estimatedfrom
thedrawings[5]of“HiloadDP1”attachmentsystem),
exposedareaaroundcontactarea
At=329m
2
,areaof
“Hiload DP1” bottom A= 27m x 27m = 729 m,
maximumdragforceatwaterflowspeedof5knots
Ft1= 1.5 MN for 8 mdraft, Ft2=1.6 MN for 10mdraft
and,
Ft3=1.7MNfor12mdraftandFt4=1.8MNfor
15 m draft. In this analysiswe used friction
coefficientμ=0.6.
The static contact force can be calculated using
equation(1)andthesafetyfactorincalmwatercanbe
calculated from equation (10) by setting
Fd=0 (see
resultsinTable3).
Itisclearlystatedfromtable3,thataccordingtoa
safety factor SF in calm water (without dynamic
forces) accounted for the tanker vessel proceeding
with4knotsspeedforward,1knotcurrentand20m/s
wind and with draft i.e. 12 m the
static force
generatedonaHiloadattachmentsystemis17.1times
biggerthantheforce
Ftfromresistance(drag)dueto
speed,oceancurrentandwindandwillincreasewith
ship’s draft. Since the estimated tanker resistance
(includingeffect of 1 knot ocean current) is 1.7MN,
the safety factor is 17.1 in this case. This evaluation
was done without considering the wave induced
horizontalforce.
510
Table 2: Main particulars and mass properties of the MT “Navion Anglia”“ during her towing operation through the
AtlanticOceanwitha“HiloadDP1”unitdockedonportsidealongside.
__________________________________________________________________________________________________
Shipparticulars:Loa=264.68m;DepthmoldedD=22.07m;BreadthmoldedB=42.5m; TankerdraftT[m]
Lpp=256.96m;Summerdeadweight=126749tons;8 10  12  15
__________________________________________________________________________________________________
Deadweight[tons]46770 68652 87751 120337
VCG–verticalcenterofgravity(frombaseline‐BL)[m]12.37 9.65 10.22 10.74
LCG–longitudinalcenterofgravity(fromaftperpendicular–AP)[m]134.88 134.09 132.30 131.28
Displacementincondition[tons]73245 95127 114227 146
812
Rollradiusofinertia[m]17.0 17.0 17.0 17.0
Pitchradiusofinertia[m]62.9 62.9 63.0 63.0
Yawradiusofinertia[m]62.9 62.9 63.0 63.0
__________________________________________________________________________________________________
Table3:Thestaticforcesandsafetyfactoraccountedfor“HiloadDP1”unitdockedonportsidealongsidetoMT“Navion
Anglia”withdifferentdraftincalmseacondition.
__________________________________________________________________________________________________
ParameterTankerdraftT[m]Unit
8m 10m 12m 15m
__________________________________________________________________________________________________
Buoyancy(ρgV)48.8 49.8 50.8 52.3 MN
Weight(F
grav=mg)45.9 45.9 45.9 45.9 MN
Netbuoyancy=Buoyancy–Weight2.93.94.96.4MN
Correctionduetocontactarea(ρgTA
0)29.0 36.2 43.4 54.3 MN
Staticcontactforce(F
s)asperformula(1)31.9 40.1 48.4 60.7 MN
FrictionforceF
fasperformula(9)19.1 24.1 29.0 36.4 MN
Resistance(drag)duetospeed,oceancurrentandwind(F
t)1.51.61.71.85 MN
__________________________________________________________________________________________________
SafetyfactorSFincalmwater,at4knotsforwardspeed,1knotcurrentand 12.7 15.1 17.1 19.7
20m/swind(asperformula(12))
__________________________________________________________________________________________________
Table4:ThesafetyfactorSFvalueaccountedfordifferent draftofthetankerTanddifferentseawavesHscondition.Inthis
analysistherewereusedshipsparticularsfor“HiloadDP1”unitattachedtoMT“NavionAnglia”attheamidships.Some
dynamicforceswereaccountedinVERESprogramusingthe
modelofsimilartankerforsignificantwaveheightsHs=2,5m
and 5 m [1]. The otherfactors were accounted using formula(10) withfixed statistical data and linear interpolation for
horizontalwavedriftforce.
__________________________________________________________________________________________________
T[m] Fs[N] Ft[N] SignificantWaveHeightHs[m]
0,51,0 1,52,0 2,53,0 3,54,0 4,55,0 5,56,0 6,57,0 7,58,0
__________________________________________________________________________________________________
8 31.9 1.50 7.06 4.76 3.52 2.74 2.20 1.82 1.52 1.29 1.10 0.95 0.82 0.71 0.61 0.53 0.46 0.40
9 36,0 1.55 8.00 5.49 4.11 3.23 2.63 2.18 1.85 1.58 1.36 1.19 1.04 0.91 0.80 0.70 0.62 0.54
10  40,1 1.60 8.94 6.25 4.73 3.76 3.08 2.58 2.19 1.89 1.64 1.44 1.27 1.12 1.00 0.89 0.79 0.71
11  44,2 1.65 9.89 7.03 5.38 4.31 3.55 3.00 2.57 2.23 1.95 1.72 1.52 1.36 1.21 1.09 0.98 0.88
12  48,4 1.70 10.857.84 6.07 4.90 4.07 3.45 2.97 2.59 2.28 2.02 1.80 1.62 1.45 1.31 1.19 1.08
13  52,5 1.75 11.798.66 6.78 5.51 4.61 3.93 3.41 2.98 2.64 2.35 2.10 1.89 1.71 1.55 1.41 1.29
14  56,6 1.80 12.749.51 7.52 6.17 5.19 4.45 3.87 3.41 3.02 2.70 2.43 2.20 2.00 1.82 1.66 1.52
15  60,7 1.85 13.6810.388.30 6.87 5.81 5.01 4.38 3.87 3.45 3.09 2.79 2.53 2.31 2.11 1.93 1.78
__________________________________________________________________________________________________
However if we take into consideration all
dynamical forces (i.e. vertical and horizontal wave
drift forces) the results obtained above are not
adequateanymore.
With reference i.e. to the horizontal wave drift
forces (
Fw) for this simplified study we can use the
results obtained from VERES program and research
analyses[1],whereforwaveamplitude
ξ=2.5mthe
horizontalwavedriftforces were consideredas 5.55
MNfor thetanker draftT=8mand to 5.05 MN for
tankerdraft10m.Forwaveamplitude
ξ=5.0mthe
horizontal wave drift forces wereestimated
accordingly as 11.1 MN for the tanker draft T= 8 m
andto10.1MNfortankerdraft10m(seetable1).
Thedynamicverticalcontactforceperunitwave‐
heighthasbeenalsoobtainedinVERESprogramand
the expected
maximum dynamic contact force per
unit
Hs was accounted as around 2.4 MN for head
waves(0°heading)andthewavepeakperiodaround
5s[1].
Itmeansthatfor
Hs=5mtheexpectedmaximum
dynamiccontactforcecanbeconsideredas:
Fd=2.4x5
= 12.0 MN.Additionally it means that for static
contactforce
Fs=40.1MN(accountedfortankerdraft
T=10 m – see table 3 or 4), the expected smallest
contactforcebecomesaround40.1–12.0=28.1MN,
whichgivesafrictionforce
Ffof 16.9 MN. Since the
estimatedtankerresistance(includingeffectof1knot
ocean current) is 1.6 MN, the safety factor from
formula(10)is10.5inthiscase(seeformula(12)).
sd
t
(F F )
(40.1 12.0) 0.6
SF 10.5
F1.6

(12)
Unfortunately this evaluation was done without
takenintoconsiderationthewaveinducedhorizontal
force. When we take into account such dynamic
horizontalwavedriftforce
Fwof10.1MNfortanker
draft T=10 m and wave amplitude
ξ= 5.0 m (see
table1)theresultofSFwilldecreaseuptovalueonly
around1.44(seeformula13):
sd
ttd
(F F )
(40.1 12.0) 0.6
SF 1.44
FF 1.610.1


(13)
511
In table 4 for the example there are some safety
factorsaccountedforadifferentdraftofMT“Navion
Anglia”with“HiloadDP1”unitdockedonportside
alongsidenearamidshipsareproceedingattheopen
sea with different sea conditions with different
significantwavesheights
Hs.
6
CONCLUSIONS
Asaresultofthisstudythefollowingconclusionhas
beennoted:
For vessel similar in size as mt “Navion Anglia”
(summerdeadweight=126749tons)maneuvering
with a “Hiload DP1” unit docked on portside
alongside near amidships area, (where the sea
fastening of HiLoad DP No.1 unit was done by
utilizing a special and integrated Friction
Attachment System fitted on board the
vessel),
withspeedforward4knots,inasignificantwave‐
heightof5.0m,thecalculatedsafetyfactorsinthe
rangefrom0.95(fordraft8m)to3.09(fordraft15
m) have been obtained, depending on the tanker
draftandHiloadDPlocation(seetable4).
FromTable4itisclearlyvisiblethatsafetyfactor
SF against sliding is bigger for the smaller
significantwaveheightsanddippertankerdrafts
(areamarkedingreencolor).
Takingintoconsiderationthefact,thatinallcases
thesafetyfactorishigherforadeepertankerdraft
‐ increase of the vessel draft should be always
considered as the most effective way to increase
thesafetyfactorinthecriticalweatherconditions.
Additionallyaccordingtothe formula(10) italso
clearly stated that the safety factor is almost the
same for both considered locations of a “Hiload
DP1” unit (forward location =0.75 Lpp or
amidshipsarea= 0.5Lpp).Howeverifwetakeinto
considerationtheexpectedvibrationduetowaves,
swelland/orcurrent
itisrecommendedtoposition
the“HiloadDP1”unitaroundamidshipsareaon
mothership.Thetransitvoyageofamother ship
witha“HiloadDP1”unitdockednearamidships
candecrease variationofthedynamic forces. For
the mother ship it was also noted that a better
headingcontrol
isachievedwithaHiloaddocked
nearamidshipsareaincomparisonwitha“Hiload
DP1”unitdockedforwardofmothership.
WhenthemothershipwasusingtheAutopilotin
a seaways during towing operation, it was also
noted, that with “Hiload DP1” unit docked
forwardthe consumption of HFO of mother ship
wasalittlehigherthancomparingwitha“Hiload
DP1” unit docked near the amidships area. The
reasonfor
thisismostprobablythefact,thatwith
HiloadDPunitdockedforwardformothershipit
was a bigger problem to keep the steady course
overtheground(COG)andourAutopilotusually
kept the rudder in fixed position turned to the
starboard side up to about 8˚to
12˚with Hiload
docked near amidships area and about 12˚to
15˚withHiloaddockedforward.
Thedynamicverticalcontactforceperunitwave‐
heightwasthelargestforsea‐stateswiththewave
peak period around 5s. In these sea‐states, the
expectedmaximumdynamiccontactforceperunit
Hsisaround2.4MNforheadwaves(0°heading).
Thevalue2.4MNfordynamicvertical
force was
confirmed via VERES simulator program [1] and
used later for our simplified calculation of SF
describedinTable4.
Taking into consideration the previous point it
means that for Hs= 5 m the expected maximum
dynamic contact force can be considered as: Fd=
2.4 x 5 = 12.0 MN.It means also that for static
contact force Fs =40.1 MN (accounted for tanker
draft T=10 m – see table 3
or 4), the expected
smallestcontactforcebecomesaround40.1–12.0=
28.1 MN, which gives a friction force Ff of 16.9
MN. Since the estimated tanker resistance
(including effect of 1 knot ocean current) is 1.6
MN,thesafetyfactorfromformula(10)is10.5in
this case.
However when we take into account
dynamic horizontal wave drift force Fw of 10.1
MNfortankerdraftT=10mandwaveamplitude
ξ=5.0m(seetable1)theresultofSFwilldecrease
toapproximately1.44(formula13):
DuringthevoyagethroughtheAtlanticOceanthe
current direction was assumed to be the most
critical when opposite to the vessel forward
motion. In such cases to reduce vibration on
“Hiload DP1” unit and increase the safety factor
(SF) for towing arrangement on mother ship we
reduced the speed forward
to maximum SOG= 5
knotswithSpeedthroughthewaterSTW=4knots.
Thetotalwaterflowvelocityrelativetothetanker
surface was assumed to be always: 4 knots
(forward speed STW) + 1 knot (ocean current
speed)=5knots(SpeedOverGroundSOG).
Wind‐generatedheadorfollowingwaves(causing
relativelylargehorizontalwaveforces)combined
with swell from aside (causing roll motions and
relatively large dynamic pressure variation
underneath Hiload DP and roll‐induced inertia
forces) were considered as the most critical
conditions when:λ> ½ Lpp for wind waves and
swellcoming
fromthe forward direction ± 20˚ to
theportandstarboardsideofmothershipandfor
windwavesandswellcomingfromshipsidewhen
λ>½B.Themaximumvibrationon“HiloadDP1”
unitwerenotedfromseawavescomingfromthe
port bow onthe relative direction
about 45˚ on
the port side frommother ship’s heading (waves
coming directly between “Hiload DP1” unit and
Navion Anglia hull). The best solution in such
cases was the reduction the speed through the
water to approximately 2 knots and COG
adjustmentto±20˚ontheportorstarboard
side.
In head waves when the vertical dynamical
contactforceistheminimum(wavehollow)‐the
wave induced horizontal drift force was acting
forwards and they were therefore be reduced by
the drag (resistance) forces acting backwards. A
critical situation appeared in the following sea
where the drag forces and the horizontal
forces
were working in the same direction and the
dynamic vertical contact force is at the lowest
level.
Therelativemotionperunitwave‐height(forHs=
1.0 m) was largest for the sea states with peak
period(Tp)intherange9–10sinsternoblique
waves (heading 135°). In these sea states, the
standarddeviationperunitHswas0.28m.Hence,
ifHs
=5m,thestandarddeviationwas0.28x5=
1.5 m, and one would expect the largest relative
512
motionamplitudestobecloseto6 m.Therelative
motions for the Fwd location of the Hiload DP
wereingeneralslightlylowerinlongerwaves.
REFERENCES
[1]HermundstadO.A.:NumericalAnalysisofHiloadDPin
Waves.MARINTEKreportno.530785.00.01.Trondheim
2011.
[2]Hiload Joint Operations ManualRev. 7 dated February
2014generatedbyTeekayforPetrobrasFieldsP‐47and
P‐57.
[3]MARINTEKReport No.609660,SHIPX Vessel
Responses (VERES) Ship Motions and Global Loads
Users’Manual,2004‐12‐21.
[4]RutkowskiG.,Hiloadtechnologyandnumericalanalysis
ofcontactforcesgenerated on“HiloadDP1”prototype
attachmentsystematcalmsea,Gdynia,2014.
[5]Teekay internal documentation: ships particulars and
drawings for MT “Navion Anglia” and Hiload DP,1
dated:2013‐2014.
[6]Transportation manual for
the transport of Hiload DP
no.1fromKristiansand,NorwaytoOffshorelocationat
Rio de Janeiro, Brazil‐being docked onto a
transportation vessel. Teekay internal document No.
1280‐KA‐O‐00001,Rev.B,dated12.07.2013.
[7]http://www.remora.no.
[8]http://www.teekay.com