7/30/2019 Formula Stability
1/25
Chapter1BasicHullFormRelatedCalculationFormula
CBLBTLBT
Cm
BT
Am
Cwp LB
Aw CP LAm
CVPwTA
TPC100
Aw
7/30/2019 Formula Stability
2/25
Simpson1st rule 1,4,1
Atleast
3offset
Oddnumberofequiwidthoffset
Simpson2nd rule 1,3,3,1
Atleast4offset
(n1)exactlydivisibleby3
7/30/2019 Formula Stability
3/25
Chapter1 Calculation
Example1:
Ashipdisplacement6000thasalengthof120m,breadth12manddraft5m.Calculate
theships
block
coefficient.
Example2:
Avessel
120
m
long
and
15
m
wide
has
adraught
of
7.5
m
in
SW
when
its
displacement
is10800tonne.Theimmersedmidship areais107m2andwaterplane areais1500m2.
Calculate(i)Cw ,(ii)Cm ,(iii)Cb &(iv)Cp
7/30/2019 Formula Stability
4/25
Chapter1 Calculation
Example3: Aship oflength240.0m,beam32.0m floatsatadraught7.20minsea
water. Atthisdraught,ithasaCB,CW andCM of 0.56,0.76and0.975 respectively.
Determineits
i) displacement, ii) TPCinseawater iii) CVP, and iv) CP
Example4: A
ship
of
length
240.0
m,
beam
32.0
m
floats
at
adraught
7.20
m
in
sea
water. Atthisdraught,ithasaCB,CW andCM of 0.56,0.76and0.975 respectively.
Determineits
i) displacement, ii) TPCinseawater iii) CVP
, iv) CPIf
the
ship
now
steams
upriver
for
one
hour
to
aport
where
the
water
density
is
1004
kg/m3,determineitsnewdraughtifthechangeinitsblockcoefficientisnegligible.
7/30/2019 Formula Stability
5/25
Example1.(WaterPlaneArea)
Aship120metreslongatthewaterlinehasequidistantlyspacedhalfordinates
commencingfromaftasfollows:
0.1,4.6,7.5,7.6,7.6,3.7,0metres,respectively.
FindtheareaofthewaterplaneandtheTPCatthisdraft.
Chapter1 Calculation
Example2.(LCF)
Ashipwaterplaneis120mlong.Halfbreadthsatequalintervalsfromaftare:
0.1,4.6,
7.5,
7.6,
7.6,
3.7
and
0metres,
respectively.
FindthepositionofCOF.
7/30/2019 Formula Stability
6/25
Chapter1 Calculation
Example3.(DisplacementwithWaterPlaneArea)
Thewaterplaneareasofashipatonemeterintervalsfromkeelupwardsare:
1730,1925,
2030,
2100,
2150
m2.
FindthedisplacementinSWat4mdraft.
Example4.(KBwithWaterPlaneArea)
Theareaof successivewaterplanesof ashipatintervalsof1.5mstartingfrom1m
waterplane are:
1531,1665,
1789
and
1900m2
.The
appendage
below
the
1m
waterplane has
a
displacementof1750tonneinseawaterandtheKBof0.55m.
CalculatethetotalvolumeofdisplacementandthevalueofKBtothe5.5mwaterline.
7/30/2019 Formula Stability
7/25
Chapter1 Calculation
Example5.(DisplacementwithTransversecrosssectionarea)
Findthevolumedisplacementofabarge48mlong,whoseunderwatertranseverse cross
sectionalareaare:
19.6,25,17.5,13,0m2
7/30/2019 Formula Stability
8/25
Chapter2CGSmallAngleStabilityFormula
KG
Verticalmomentofallshipmassesabt keel
Allship
masses
LCG
Longitudinalmomentofallshipmassesabt midship
Allship
masses
TCG
Transversemomentofallshipmassesabt centreline
Allshipmasses
KB
Allverticalmomentabt keel
Totalmoment
7/30/2019 Formula Stability
9/25
Effectonmassshifting
xmGoG1
ymGoG1
Effectonmassaddition/removal
f
xm
GoG1
f
ym
GoG1
7/30/2019 Formula Stability
10/25
Suspendedmasscalculation
Kg ofthe
suspended
mass
taking
from
the
point
ofsuspensiontokeel.
Momentofstatical stability=Rightingmoment
GZ
sinGMT
7/30/2019 Formula Stability
11/25
Angleoflist
Momentofstatical stability=Rightingmoment
GZ
sinGMT
L
T
101
GM
GGtan
7/30/2019 Formula Stability
12/25
FreesurfacecorrectionFSC
FSC
I
12bl 3
GMTeff FSCGMT
7/30/2019 Formula Stability
13/25
Chapter2 Calculation
Suspendedmasscalculation
LCGcalculation
MassshiftingcalculatenewKG
Massaddition/removalcalculatenewKG
Example
(from
Notes
Pg 3)
displacement,
GMT,
LCG
7/30/2019 Formula Stability
14/25
TutorialQuestion1:
Ashipwhichistobemodified,hasthefollowingoriginalparticulars:
Displacement 150.00t
GM 0.45m
KG 1.98m
KB 0.9m
TPC 2.00t
Draught 1.65m
Aftermodification,20tisaddedatKgat3.6m.CalculatetheGM,assuming
constantwaterplane areaoverthechangeindraught.
Chapter2 Calculation
TutorialQuestion2:
Ashiphasadisplacementof10000t,KG7m,GM0.2mandwaterplane area1600m.
Asumming KMremains
constant
throughout,
calculate
(i) ThemassofdeckcargothatcanbeaddedatKg13mwithoutmakingthe
shipunstable,&
(ii) Thechangeofdraughtiftheshipmovesintofreshwaterofrelativedensity
1.004after
loading
of
cargo
in
S.W.
2
7/30/2019 Formula Stability
15/25
Chapter2 Calculation
TutorialQuestion3:
Avessel,havingadisplacementof11900tonne andGM0.85m,hasalisttoportof
2.75degree.100tonne ofcargoisstilltobeloaded,andtwocompartmentsare
available,one
6.1m
off
centreline to
starboard
and
the
other
8.4m
off
centreline to
port.
AssumingKMisconstant,calculatethemassrequiredineachcompartmenttothe
vesselupright.
7/30/2019 Formula Stability
16/25
Chapter3LargeAngleStabilityCalculationFormula
GZ
GZf
sinKGKN
cosGGsinGGZG 211000
G0G1.sin
/G1G2/.cos
Signconvectionsapply!
7/30/2019 Formula Stability
17/25
Curve of statical stability
1. Range of stability
2. Angle of vanishing stability
3. Maximum righting lever
4. Initial GMT:
=0tov
=v
=GZmax
Drawtangenttocurveat =0,drawverticallineat =1radian(57.3o)totangentialline,verticaldistanceisinitial GMT.
7/30/2019 Formula Stability
18/25
Chapter3 Calculation
Inacertainconditionofloading,theshipdisplacementismadeupasfollows:
Afterloading,followingchangestookplaceagain,
2000tonneisremovedfromalocation,whichis5mfromkeel.
Additionally,2000tonnecargowasloweredby2mtowardskeel.
Item Mass (t) Centre of Gravityfrom Keel (m)
Lightship 5000 6.00
Cargo 6000 3.00
Fuel 2500 2.00
Store 1500 5.00
7/30/2019 Formula Stability
19/25
Chapter3 Calculation
Item Mass (tonne) VCG(m)
Lightship 4 200 6.0
Cargo 9 100 7.0
Fuel 1 500 1.1Stores 200 7.0
TutorialQ1:
TheangleofinclinationandcorrespondingrightingleverforavesselatanassumedKGof
6.5masgivenincrosscurvesare:
In
a
particular
loaded
condition
the
displacement
mass
is
made
up
as
follows:
Plotthecurveofstatical stabilityfortheinformationobtaineddirectlyfromthecross
curvesandalsothemodifiedcurverepresentingstatical stabilityattheactualloading
condition.Determine
the
initial
stability
and
the
range
of
stability
for
the
loaded
condition
given.
7/30/2019 Formula Stability
20/25
Chapter3 Calculation
Ashiphavingadisplacementof9500thasthefollowingGZcurve
0 10 15 30 45 60 75 90G
0Z(mm) 0 210 401 822 918 802 410 -430
Followingchangesinloadingtakesplace
a)60tonnes ofcargoshifted horizontallythroughadistanceof13m
b)120
tonnes of
cargo
shifted
vertically
downwards
adistance
of
5m
Draw(1)theoriginalGZcurve,
(2)theeffectonGZcurveof(a)alone
(3)theeffectonGZcurveof(b)aloneand
(4)theeffectonGZcurveofboth(a)and(b)simultaneously.
7/30/2019 Formula Stability
21/25
Chapter3 Calculation
Tutorial Q4For a particular ship of 1500 tonne displacement the GZ curve is defined by
the following relationships:
o 0 15 30 45 60 75 90
GZ(mm) 0 52 195 310 172 -24 -370
During a storm 100t of cargo shifts horizontally 5.0m and 2.5m verticallydownwards. Determine,
a) the angle of list and
b) the range of stability.
7/30/2019 Formula Stability
22/25
Chapter5LongitudinalStabilityFormula
t AF TT tc of tt
TM tM ii dm Massshifting
TM tM LCFlcgm ii Massaddition/removal
MCTCL100
GMLMCTC100M ttc
TPC100mdTp
TFf TFf
TFf TFf
LCF
2
L
L
tT cF0
LCF
2
L
L
tT cF0
LCF
2
L
L
tdTT cpF0
LCF
2
L
L
tdTT cpF0
7/30/2019 Formula Stability
23/25
Chapter5 Calculation
Example1
A160mshipfloatsatanevenkeeldraughtof8.20m. Itdisplaces17600tandhasa
KGof12.0m. Atthisdisplacement,KMLis157.0mandthecentreofflotationis1.80
maft
of
amidships.
To
have
agreater
immersion
of
the
propeller,
three
containers
of
masses16.0,14.0and12.0tareshiftedaftwards throughlongitudinaldistancesof
90.0,80.0and70.0respectively.
Calculatethefinalforwardandaftdraughts.
Example2
Aship,160.0mlong,displaces3600twithforwardandaftdraughtsof1.50mand
3.60mrespectivelyinthelightshipcondition. Atthisdisplacement,thecentreof
flotationis2.40maftofamidships,TPC12.0andMCTC120.0tm.
Ahelideck,ofmass60.0t,istobefitted65.0mforwardofamidships. Determinethe
forwardandaftdraughtsinthelightshipconditionaftertheinstallationofthe
helideck.
7/30/2019 Formula Stability
24/25
Chapter5 Calculation
Example3
Theforwardandaftdraftofavessel,76.2minlengthare5.18mand5.64mrespectively.
Themaximumpermissibledrafttocrossabaris5.5m.Calculate,usingthedatabelow,
themasstobedischargedfromaposition26maftofamidshipstoenablevesseltocross
thebar.
TPC:12 MCTC:91.5tm LCF:1.52maftmidships
Example4
Avessel
of
200m
length,
floats
at
draft
of
7.5m
aft
and
7.3m
forward.
Subsequently
followingloading/unloadingtakesplaceataport:
Loaded: a)390tat15mfwd ofmidship
b)450tat3maftofmidship
Unloaded: c)130tat
16m
forward
of
midship
d)100tat5maftofmidship
Baseyourcalculationsonthefollowingavailableshipshydrostaticdataforthisloading
condition: LCF=2.9maftofmidships TPC=22t MCTC=199tm
Calculatethe
final
forward
and
aft
drafts.
7/30/2019 Formula Stability
25/25
Chapter5 Calculation
Example5
Avessel146mlongfloatsatdraftsforwardandaftof5.14mand5.2mrespectivelyin
waterof
desity 1025kg/m3.
Thefollowingcargoisloaded: 400tat12mfwd ofmidship
600tat18maftofmidship
Usingthehydrostaticdatagivenbelow,caculate thedistanceanddirectioninwhich60t
ofballast
must
be
moved
to
give
afinal
trim
of
0.36m
by
stern,
and
the
final
drafts.
Hydrostaticdata:
LCF=3maftmidship TPC=20 MCTC=150tm
Top Related