DEFI\ITION PERTAINING TO HYDROSTATIC PARTICULAR5

.-.!iil of a substance is its mass per unit volume, normally expressed: :-.:...s per cubic metre in ship calculations.

:: ::i|e Density of a substance is thc ratio between the densit\- of that- .':'ie and the densit)' of fresh rvater.

.:lecement of the ship is the weight of the ship and its contents or?iqht of water displaced b)' the ship in tl.Iat condition.

.:.iacement = Underwater volume of the ship x thc density oI the rn,aterin which she is floating.

- uld be noted that the volume of displacement is the underwater.:rrr of thc ship. When a ship proceecls frofr water of one dcnsitv

::cr of another density, the volume of displacement ciranges, whereas,r:splacement remains unchanged.

::.:rostatic Dlaft Or True Mean Draft is the dra{t at the centre of f loatation.:r the ship is on an even keel, thc drafts forward and a{t, the mean

. n ( l the h ]J ros td t rc d rd l t a re a l l the ramr ' .

. a (Tonnes per centimetre Immersion) at any dralt is the weight in::i hhich should be loaded or discharged to change the vessel s mean.: l.\' one centimetre, in saitwater.

TPC _ 1.025 x Area of ship's water plane

100

\ICTC or MCT 1cm (Moment To Change Trim By One Centimetle)- ::-.! moment required to change the toial trim of the vessci bv one

: _ : : t ] c f f e .

W X GN{LMCTC 100rL

--5 icentre of Buoyancy) is the geonetric centre of the underwatcr volume::re ship. The entire buoyancy provided bv the displaced l\,atcr mav-,.nsic1ered to act vertically upwards through this point.

--B (Longitudinal Centre of Buoyancy) is the longitudinal separation..rn the After Perpendicular and the cenke of buoyancv.

(\rertical Centre of Buoyancy) is the vertical separation beti-ccn the.r.d the ccntre of buoyancy.

' . aB

CF (Centre of Floatation) is the centroid of the sirip's watcr plane area.

LCF (Longitudinal Centre of Floatation) is the longitutl inal scparationL . . , . , e r , ' l , . A j i - - t r r r , , r r , l i r r ' : - . J t h , C e ' t r . , , i l l n a t . r L i o r ,

M (Transverse Metacentre) is the point of intcr'sectior of the lertic;rl l inesthrough the Centres ol BuovancL in the upright conelit ion ancl ihe rerhcall inc through the ccntre of Buovanc,, h slightlf inclinecl conclit iurr.

KM is ihe rertical separ.l i ion bet('ccn thc kccl and the transverse lnetacentre.

M, (Longituclinal Nletacentre) is ihe poinf oi intersection oI lhc Yerticailine thloullir ihe Cenhe of Buovar\c! in thc cvcn kccl conclition anri tl'rcvertical linc through thc Ccntre of Buortrnc,v in a slighth' trimmccl c(mciitior.

KML js the |ertical separation bet\\,e{:n the keel and ihe iongituclin;rllnelaa-ar1rac.

GM (N{etacentri. Height) is thc vcltical scparation betlvecn the centre c.i

" r . , r r . , n , 1 r l . , . , ' ' . - ' c " . e n r r ' ' . ( n t r (

\OT}-: In stabilitv calculations in various text books, the differentl.','cLostaiic particulars like TPC, lllCTC, LCF, KIVI etc. are assu!1e(l collsiant.iespjte change in dlsplacement/diaft, to facilitate easier solutjon. This.issrnlption is incouect and cannot be usecl $'hile pracLicalh, c.rlculatingstabilitl/trim on boarrl slrips. it i11r.rst therefore, be borne in mincl that.rl l thc h|clrostatic farticulars of t ire ship .hatlge w,ith draft/clisplacement.'I i Ie

.alcuLrtions i i this book havc taken this important fact into.iccouilt.

if :iroui,-l also L,.e noteJ that though the .lisplacenent rcmains unchanged,icr sornc of thc h\'clrostatic palticulals ci1ange lvith densit)' of u'atcr inir'ficir the ship is floating. Even u'hen the densitv ar-rd the clisplacement'rli. con-ctant, some of thcrn likc KNI also change with HEEI- and TRIN.I,.rs the sllap-e of rraterplane alters r.r'hen these parameters change. ThisIact has bcr:n takcn into considcration in problems on LIST/HEEL, t 'here::r. \'alue oi KN'l is assumed constant onh for very sma1l angles ot heel.

DETERMINATION OF HYDROSTATIC PARTICULARS

Displacement

%{3

9540 ?

9788

440

Interpolating

diff. inH)'drostatic

diff. in MCTC

H1'droslatic TPC MCICDraft

,1.&) n.9 M5.1

5.00 22.08 166.8

0.2 0.09 1.1

as above, we have:-

0.2 t 192

73.016 72.9-17

0.002 0.057

LCF VCB KM K1\4,

73.0t8 72.974 2.576 9.032 257.3

2.684 8.890

0.108 0.1J2

247.7

9.6

For diff. in dispiacement of 440 t diff. in \drostatic draft = 0.2 m

For cliff. in displacemcnt of (9540 - 9348) = 192 r diff. in hvdrostatic

clraft.

draft

diff. in TPC

= 0.087 H1'd. draft = 4.80 + 0.087 = 4.887 nt

0.09 x 192-a0

= 0.039 Trc = 21.99 + 0.039 = 2zn9 t

'1.1'< 192= 440

= 0.611 MCTC = 165..1+ 0.611 = 16r'J711 t

0.002 x 192diff. in LCB = = 0.001 LCB = 73.018 - 0.001 =73.017nt,140

0.O57 x 192ciiff. in LCF = = 0.025 LCF = 72.947 - 0.025 : 72.919 m440

0.108 x 192= 0.047 vcB

I I

diff . in VCB =440

= 2.576 + 0.017 = 2.623 m

diif. in Klt I 0.062 KM = 9.032 - 4.062 : 8.970 tt

diff. in KNI, 4.189 KM, = 257.3 - 1.189 = 253.11'1 nl

Displacement TI{

15693 23.29

16161

468

0.112 r 192-l{0

9.6 x 1924.10

0.20

0.199 x 0.06

H\.drostatic

Dratl:

7.60

7.66?

7.80

0.20

MCTC LCB LCF VCB K]VI KM,

191.8 72.690 70.979 4.0,10 8.238 178.9

23.41, 191.6 72.641 74.780 4.1,11 8.240 176.6

0.12 2.8 0.0,19 0.199 0.104 0.002 2.3

Interpolating bet$.een the abole valuesi-

468 r 0.06Di f f . i n . l r -p . = l l 0 . I' l ) .2 \ )

0.12 x 0.06Di i f r r r l l t 0 r l ro

t , l t l

2.8 x 0.0t1Dif i. in \ICTC = - = 0.8'l

| / \ l

Drsp. = 1 tb9? + 1 l l l .4 :15833.4 f

TPC = 23.29 + 0.036 = 23.326 f

MCTC = 1?1 9+0 9Ll = f r1 .611r t

= 70.979 - 0.060 - 70.919 kl

0.0.19 x 0.06Diff. in LCB = 0.015 LCB = 7:690 - 0.015 - 72.675 ttr

Diff. in T-CF : o_

= 0.060 LCF

0.10-1 x U.06- --1'ru.. -- = 0.03r VCBDiff. in VCB

t l

= 1.0,10 + 0.031 = 4.071111

Di{f . in KM

Diff. in Klvll

= 9oo2' ! 09 = o.oot

2.3 x 0.05= o2o

= 0.690

KM = 8.238 + 0.001 = 8.239 nt

KM, = 178.9 - 0.690 = 173 210 m

t 3

DETERMINATION OF HYDROSTATIC PARTICULARS IN WATEROF DENSITIES OTHER THAN SALT WATER,

It shou](l be notecl that the hvdrostatic particulars supplied are forthe vessel floating in salt i\iater. When the vessel is floating rnlvatel of any other dcnsity, some of the tabulated particulars u'illalier as sho$,n below.

DISPLACEMENT The clisplacement ai a particular clraft i.e. a particularunderwater volume obvicluslv varies directly as thedensitv oi the water. THUS DISPLACEMENT I!DIRECTLY PROPORTIONAL TO DENSITY OFWATER. At a draft of 5.6 n.r in SW, the di.:(from the tables) = 11120 L, therefore

Disp . in RD 1 .0151.015= 11120 x lO25

= 710"1i

TPC For an immels ion o f 1cm, a tthe volume of water displacecltherefole tirc TPC (the weight offor 1 cm imrnersion) WOULDAS TIIE DENSITY OF THE

1.015TPC = 22.32 x

lO% = 22.10 t

MC-TC Though the density of rvaterKM. which is equal to KBthe under\4'ater shape andas weil as the shape of thefor a par t i cu la r t l ra | : t remains ur . i . -of the change in the densitvif the KG is unaltered, thethe same. The ler.rgth of theline also remains unchangec

expression, MCTC

a particula:rematns rr.:

waler disp..:VARY D. i

WATER

I 4

the only parameter that changes when the densit)' isaltercd, is the displacement W, which varies directly asthe density of water. Thus MCTC at a particular clraftVARIES DIRECTLY AS DISPLACEMENT i.e. DIRECTLYAS THE DENSITY.

I n lqVCIL = 1710 . -= - 16q33 mt

T.UZ)

LCB LCB depends on thc underh-ater volumc and its shap.,u'hich ate unaltered.

LCB = 72.992 n (UNCHANGED)

LCF LCF depends on the shape of the water plane whichrcm: inc r rnrh:nop,- l

LCF = 72.675 tt (UNCHANGED)

VCB VCB depends on the shape of the unclerwater volunre,which remains unchanged.

VCB = 2.998 rfl (UNCHANGED)

KM KM = KB + BM, depends on the underwater volumeand shape as weli as the shape of the vessel's \4,aterplane.Since these have not altered,

KM = 8.578 l'' (UNCHANGED)

KM. As stated for MCTC, the KML will remain unaltered.

KM. = 223.s l'l (UNCHANGED)

l 5

CALCULATION OF HYDROSTATIC DRAFT FROM DRAFIS FORDAND AFT

1 For a vessel \,vith uo trim, the clrafts forcl and aft is thc rneandraft as r,vell as thc hvcirostatic clraft.

2. For a vessel rvhich is trin-rmccl, obtain the arithmetical mcan draft.Determine thc position of LCF for this mean draft.

J. Calculate the l{ydrostatic draft as belo\,\,:

I-lyclrostatic draft = draft aft (1) correction, $'here

trimr LCFCorrcction

LBP

Notcr (i) Corrcction is -r'c r.r'hen trimmed by the stcrn,

+ve when trimmed L]y thc head,

(i i) Corrcction is unaffccted b\, densitv of water, in lvhichsh ip i5 ; lnn r ;n* .

' l Fro:r the h\.irosi.rt ic tables, ,rnv required hl clrostatic piuiiculars canL)c dr.tenr..r: ' ,cJ .rg.rinst th. h|clrostatic draft.

KG BY MOMENTS AND FINAL GM

ln considering a shiprs stabilitv, ihe GM is an important criterion. GMis the vcrtical separation between the centre oI gravity and thc transversenetaccntre of the ship, that is KM - KG.

As indicated in the earlier problcms, the KM for any displacement is avaiiablelrom the hydrostatic tables.

The KG of the vessel is usuallv obtained bv the principle of moments.Thc moments arc taken about the keel of the vessel. The vertical momcntof the ship's displacement is obtailled as the product of the displacementand the KC (not thc KG corrected for lree surlace cfiect) Thereafter,such calculations may involve three opcrations, i.e loading, clischargingancl shifting.

Moments of u'eights loadecl are added and those of rveights discharged,subtracted. When a weight is shiftcd, the change in the moment aboutthe keel is obtained as the product of the weight shifted and the \,erticaldistancc through which it is shiftecl. This quantitv is added rvhen rr,cightsare shifted upwards and subtlacted when weights are shilted downwards

Final MomentFinal KC =

Final Displacement

Frcc surface of liquid in any compartment causes a virtual rise in th!centre of gravity ancl, therefore, a corresponding virtual loss in the G\lof the vessel. Therefore, this corrcction (FSC) is subtracted from GM (Solirlto obtain GM (Fluid). Conversely cM (Solid) can be obtained br- acldingthe ISC to GM (Fluid). The FSC is customarily applied to the CM anunot to the KC.

FREE SURFACE CORRECTION

As stated eariier, a virtual risc in thc CG and a consequent virtual loss

of GM occurs whenever there is a flee sulface of liquid in anY compartment

r r r th , .h ip . lh i . los ' i . no t Presen l i r lhc Lank is e i rher compl ' le l r

fuli or complctelv emPty, as therc is no tree sLrrface of lilluid in either

of the conclitions. ThL lirtual loss in GM is obtaincd bv the c\Presqion

\'Vhere i = moment of inertia of the frce sulface area

V = undenvater volume of the shiP

6t = densit)' of iiquid in thc tank

5s = densitY of water in which the shiP is floating

i x6 tVAs

The numerator (i x 6t) is refcfred to as the

th(' .lenominator (V r iis) is the disPlacernent of

being the ship s displacement, is independent.

Free Surface Moment andthe ship. The denominatolof the densitl' ot water rn

"'fli.i tn" snip is floating lhe moments of inertia for the various tanks

are available on page 18 of the Booklet oi Trim and StabilitY particulars

of \1.V. 'HindshiP .

The moment of inertia of each slack tank is multiPlied bi/ the dcnsitv

of licluicl in that tank to obtain the free surlace moment The total free

surfaie moment dividecl b,v the disPlacement, as shown on page 19 oi

tl.r" ubou" booklet gives the virtual l'css in GM or FSC FoT a particular

Ji.ptu.",rr".,t, FSC is inclependent of the densitl' o{ water in u'hich thc

ship floais.

^/

FORE & AFT SHIFT OF G

\\'hen finding moments about AP, moments of u,eights LOADED are ADDED:ntl rhose of weights DISCHARGED are SUBTRACTED.

\l hen rveights are shifted in the fdre & aft direction, the moment of thesliitt is obtainecl as thc product of the wt. shi{ted and thc horizontal clistancethrough \\'hich it is shifted. The moment is ADDED if the rvt is shiftcclFORD and SUBTRACTFD if the \\,i is shifted AFT, on the same principle,rs for moments of u'eights shifted vertically, u,hen consiclering moments.1bout lhe keel.

-L:' or1lv one weight is loacled, dischalged or shiftecl, the si-rift of G,iiG may be calculated by thc expreisions

\ \ ' x d n ' x c l r v rd'- =

l\."", 'n lor 1r rcsPectively, where W is thc original clis-

. :.-!nrcnt and w _the r.,'eight loadcd dischargccl or shiftccl For loacling'.r Jischarging d' is the athwartship distanic beth,een g oi the wcight: -r G of the ship. ln the case of shift ing, cl, is the athllartship Llrstaicc:.rgh \\'hich the \,\,eight is shiftetl. For an uprigllt ship, C is on the' i r ! l l n e .

i : l l l l l o t e

. a lau la tc

'- rcsultant:Iarncnts

:alacement

ATHWARTSHIP SHIFT OF 'G' AND LIST

than one h,eight is in.,'olvecl, it h,ould be nlore convcnierltCG, bt' momcnts aboui the centre line.

moncnt about the centre l ine obtained as thcto port and moments to starboarci, clivicledgives the athwartship GG,.

ai!Jebraic sunrbv the final

::,rm lhe figure it can be seen that the iist may be calculateci by the,.rression

tan 0 = GG,GN,l (Fluid)

r-r abovc formula can be used without appreciable loss of accuracy for:n small angles of list only because, as ihe lists, her l^,trrer plane area

::.rnges causing a change in her KM anrl consequentll. her iM. Lists: iarger angles can be correctly determine<i bv piotting her heeling arm

rj:r'e ovcr her curve of statical stability, as 'shown,

iater.

' t9

r': Righting Lcver GZ is the perpendicular distance between the ship,s:.tre of Gravity and the vertical line through the Centre of Buoyancy.:n inclined condition.

. ltighting Moment or Moment of Statical Stability of a vessei at any' : r of heel is the moment with which she tends to return to the original-: cht condition, when heeled to that angle by an exteinal force.

RIGHTING MOMENT

.:r| small angles o{ heel, GZ = GM x sin g

:.:-ger angles of heel, GZ must be obtained as

- .orrected KG x sin 0)

:::-j Moment = W x GZ

':qlrt ing Moment = W x GZ

-Z for 100 heel in condition No. 4 = 0.262 m

: -':'-"iore Righting N{oment = .19617 x 0.262

l:lhting Momeflt = 5139.65 mt

RELATIONSHIP BETWEEN DENSITY, DRAFT & DISPLACEMENT

'Ihe Student is advised to refer to definition of DisPlaccment, Volume of

Displacement, Density and Relative Densitl', given earlier in this book

LAW OF FLOATATION: Everv bodY floating in a i luid, cllsplaces avolumc of that fiuid equal in mass to the mass of that boci

Thcrcfore, in the case of a ship, her Displacement = lVeight ot rvatclclisplaced.

Thc r,r,eight of an\. substance = It's volume x it's clensitv. Thus the lVeightof tirc ship : Volume of u'ater displaccd bl the ship x DensitY of thai\\'atet.

lV=Vxd

Whcn a ship proceeds from \\ 'ater of one densit) t(l \\ 'ater (ri anotherLlensit\', her displacement cloes not altet. Thereforc from the above erprcssionit can be seen that W remaininfl constant, V, thc underwater vollrrne andthcreforc the draft must ir-tcrease if the density of t'ater dccreases, anclconverselt 'the unclenlatcr volume anci the clraft must clccrease if the Llensltvincreases.

It shoulcl also be notecl that the displacement oI a shiP {loating at thcsan-re draft in watcr of different densities, lvill not be thc same as thcunclelrvatet volumes would be the samc, but the dcnsities are tiilfelent

Thc Fresl.rwater Allou ance of a ship is the number of millimctres bi' rvhichthc rlean clraft of thc ship changcs when she proceecls {rom Salt Waterto Flcsh Water or fron Fresh Water to Salt Water, when iloating .rt theLoad $'ater l ine.

.1TPC

Thc FIVA given in thc Load Line Ccrtificate is valicl onlt' for clraltscoresponding; to \\'aterlines bctu'ccn W & TF marks. For clrafts less tharr\\'inter ciraft thc FWA for the concernecl tlraft mav be calculatetl bv thcaboye expression using lV and TPC, both in salt lvater at that (lraft

Dock lVater Allon'ancc foi clensities bctu'een those of FW ancl SW n-raybc obtained bv simple proportion.

IIVA ' (Differcncc in densitics)

Calculations in this sectioll 1r1av also be clone\'olume, densit\ , ancl weight.

Fl\iA (in mm)

Thus, Dock Water Allon'ance = (1.025 - 1.000)

using first principlcs of

RIGHTING MOMENT USING KN VALUES

The student should recall thatobtained as GM x sin 0.

At larger angles oI heel, GZ

KN - (Conected KG x sin 0)

at very small angies of heel, GZ nrav be

must be obtained as

As can be seen from the figure, GZ = PN = KN - KP

= KN - (KG sin e)

From thc Iigure, it appcars that GZ couid be obtained as GM sin 0 forar-n' angle of hccl. It cannot be done in practice, as the GM changesrr,'ith thc angle of ireel. The changc in GM is caused, due to changei1'r thc positiorl oI N,I with heel. Sir.rce this change is negligible for smalangles of heel, GM mav be consiclered constant at such angles of heel.

Thc hvcirostatic table provides the KM for the upright condition onlt anclnot for different angles of heel, but the KN is available for various anglesof hecl. Therefore GZ can be obtained vcry correctlv from the expres:iorrKN - (KG sin e), for anv angle of heel.

The siabil ity particulars provided on ships give KN values at cli l lerentclisplacements at convenient intervals of heel_ For intermediatc values ofLlisplacement antl heel, KN values mav be interpolatccl linearlv u,ithouiappreciablc loss of accuracv.

1 6

TRIM - is the difference between the fold draft and the after draft

CENTRE OF FLOATATION: (CF) is the centroid of the shiP's water Planearea. The ship trims about this Point.

CALCULATION OF TRIM: Since the hydrostatic Particulais of the vessel

are available, the trim of the vessel can be calculated accurately by the

method explained belorl'.

When a ship is in static equilibrium, the buoyancy provided by the disPlaced

rvater is exictly equal to the ship's weight. When_ the Centre of Bugyancv

ancl the Centre of bravitl' are in the same vertical line, these forces produce

no couple and tllerefore the ship is in static equilibrium at her present

trim.

buo\ANcY

l , ' ? , - - - - r

c,

Lut - Lt c)

\{,:16, H i-

When the centre of buoyancy and the centle of gravity are not in the

same vertical line, as shown in the figure, these two equal and oppositeforces set up a couple tending to trim the vessel The moment of this

couple i.e. Trimming Moment, is obtained by the Product of one of the

forces and the lever betrveen the forces i.e (LCB - LCG) x clisplacement.The Trimrning Moment divided by the MCTC gives the total trim of theship in centimetres which is then divided by 100 to Sive the trim inmetres,

Thus Total trim 't' metres

TRIM

(LCB - LCG)x displacement

MCTC x 100

figure the trim obtained would be by the stern.

LCG the above formula would result in a negativethe head.

As can be seen flom the

If the LCB was less thantrim indicating trim by

l 8

As shown in the above figure,

LCF as the total trim bears to

txLCF

Iafter trin would bear a ratio to the

t tiength of the ship, i.e. _--r^ - -

LCF LBP

_ tx (LBP-LCF)LBP

t - t" and vice

the

the

Similarly t,

Also tr

t

versa/

\ ' - - -

1 .

)

NOTES TO CALCULATE TRIM OF VESSEL AFTER

LOADING/DISCHARGING/SHIFTING

For a vessel $'ith no trim, ihe aiithmetical mean draft is the same

as the hJ'drostatic draft

for a vessel $41ich is trimmed, obtain the arithmetical mean draft

Determinc thc posiiion of LCF from AP, for this mean draft'

Caiculate the h,vdrostatic dralt as below:

Hvclrostatic diaft = dralt Aft t correction, where the co{ection

I r tm v L l t

LBP

Note: Correction is -ve when trimmed b,v stern

+ve $'hen kimmed bY head

From the hvdrostatic tables, determine against the hydrostatic drafi;

the corresPonding displacement (if not given)'

Lisi the various rveights involved in arrivjng ai-thc final. disPlacement'

r i z , o r tq in r l L l i sp la .cnren t , wcrghts l "adcd d i ' charged or sh i f ted

tog"tL"." *',tn lherr Lcg Calculate the final longitudinai moment

and final clisPiacement

Iind the LCG from AP as follows:

3.

.1.

) .

I-CG from AI' - FinaL Lgngtmomenls-

Final disPlacement

6. Determine against final displacement, the values of H-vdrostatic draft

MCIC, LCB and LCF.

LCB _ LCGx Displacement

7. Total trim t' (metre) NICTC x 100

't ' x LCF8.

9 .

Trim aft t"' (metre)

Trim forward 'th' (mehe)

Draft aft

Draft fwd

LBP

Hydrostatic

Hydrostatic

draft + 't,'

draft - 't,

8 0

The hydrostaticat the Centre

draft of a ship is her hue mean dlaft, that is,of Floatation.

AB (corrn. )

the draft

stern. Heralso be seen

cD (LBP)

In the case illustrated above,hydrostatic draft is after draft

the vessel is trimmed by the- the correction AB. It can

from the similar triangles ACD and ABF, that BcF (LCF)

LCFCorrn. x LBP

.. Colrn. to A draftTrim x LCF

LBP

Since, Length of the ship is constant, the corrn. will vary directly as LCFand also directly as the trim.

The student should be able to visualise that when the vessel is trimmeclby the head, the hydrostatic dralt will be After Draft + the correction.

As can be seen from the above expression, the correction to the afterdraft is independent of the density of water in which the vessel maybe floating.

8 l

CHANGE OF TRIM DUE TO CHANGE OF DENSITY

r:r student is alreadl.aware that the h),drostatic draft of the vcssel changesrcn she proceeds from water of one clensitt- to l\,ater of ur-r,,,r-r". .r"r,"r,y.::. should further notc that the trim of the vcssel also alters \.!,ith the-i:rge ()1 Llcnsity. As can be seen from the follou,ing problern the ctrangenim,is caused Llue_ fo the change in the vaiue of f_CS', u, tn" htd.ostatic-- r (nange\ rvrfh change uf rlensitr,. Since the value of t,CB changes,

. lotal trim obtained bv the formula, , : (iara -Iry, #

- w also changes.

:rLrl( 's are:_ i t l l e< ]

: : ( r l 100

USE OF TRIM TABLES

providecl indicating changc i11Ltalts, whclt tanks are filled k)

i weight. at cl i f fcrent posit ions

l.ri'ics r-nav bc: rrr t l ischarging,: ncights shifterl'x. postt i()tr and

' : i . l i 'rc notccl that morc accuratc results arc-ir:nied. in_ the carlicr problcms. lvhen largc' ' olved, this nethorl shoulcl not be usec1, ;s-rrue ot ]vlCTC rnaY change cor-rsiclerablt,.

u . , ' L l f , ' r JL l e r r r r i r ra t ron , , r aPp Io r i rn . t t L . J rn f t . . r f t . rwcights which are not large. l.hc tables c.Ir bealso/ as rt can bc consi(lerecl as thc lvcighi clischargcr.l

then loaclcrl nt the othcr posirrol.t.

draft For\a'arcl ancl Aft attherr capacit) ' ancl also forrvith respcct k) miclships.

obtairlecl bY calcuiatjonschangcs in displtceur(]ntthe positiorl of CF anci

CURVES OF STABILITY

cRoss cuRvES oF STABTLTTY (KN CURVES)

l h(, stlr(lent is aift 'arlv fartri l i .tr lf i th thl. Righting Le\'cr CZ, \\ 'hich is nrL.lsur!.f lom the ccntfc of gravii\. It can bc seen irorr thc above tigurc flt i :KN is ihe righting leler as measurcci irom the kccl. Thc lalucs oi K\\r1l ran u'ith heel anLl displacement.

Closs Curles ol St.rLri l i tv nlc .1 set ()f clrrvcs oi KN valuts ploitcd .rq.tir.ts:. i scnlc of t l isplaccnrcnts for various anglcs of l1eel. I-h.se curlcs f.tcl l i tatlobti l inir-ri l oi KN Ialues, at an! disl 'r lacemcnt, for thc pat-ticular arlglcicrf het.l for rrhich tltc curles arr clrarvn. lhc student slloulci lcrjf i thisfor hirrsdf b\' l lspecting the Cross Curves availrtrlc in the l 'r irn & Stabil ihpnli iculars of Nl.\r. l l lnclship or anv othcf ship.

Vcr\ often, KN valucs are also givcn in a tabular fornr in addltion k)th(' cr-rr\ 'es, as in thc case of N1.\/. Hirrrlship Thc ntain usc oi K\r,rlues is to obtain GZ for an| KC, at anv displ.tcernerrt, for ciifft,rc,ntanglc of heel. Frorr thc above iigurc it cau Lre sccn thrt th!' GZ atan\' .r l lgle ot hr.:ci mat' be .)btainccl bv tl-re erprcssion CZ = KN (KCsi11 0). Froll the CZ r'.r lucs obtair-red at thc differcnt anglcs of hcr.:I,i t 1s possiblc to construci ihc cuI!e oi staiical stabil it i . ior thlt cou(1lrl(nt.

Curve of Statical Stabil ity

This is a curvc of CZ valuesciisplacencnt n ncl a part icul:rr& Siabil i t l palt iculars of nl lcurvr of st i tLical stabil i t \ ' , i t

plotteci against a scale of hcel for a pat.t icul lr-KG. Sucl-r curvcs are i l lai lalr lc in t] ic lr inrships for thc Yarious contl i i ions. l i .om ais possiblc to ascettain thc fol lo\\ ' i11gl

heighi, (G\,1 fluid).a) Thc l lr i t ial nctaccntric

Llonc in practice - as thc CNl fourrd is l ikelr

I t l

Note: l l i is shoulcl not Lre

ro De verY inaccurate.

Thc angle of contrafiexure fi.erate of increase of GZ u'ith l"':h:- "iq]"

of hecl upt. i'hich ther r ra ' incrr . . r*e i r , : , t " i i , , . .

'J . l i " " " r r - r \

In(re ' r \ i r lg r l l rnuglr r l rc cZ.rr r,hi,,an!r, , fr," ";;l; ;;': ;i,-.1il.1';: Lll j.:ll'J"1.,;l:.j;:;:r I l t ( c t , l l r . h i c l r t h L . . i e c l L . J g , , , l l t m c r \ e \ .

]i;.,i]l'::.lll ", \,alL,o of thc vcsser ancl the angle of hccl at

fhe anglc oI lanishing stabil it\ ' an(i t l .re r.tnge oi stabil itr,.

,f].,.L,_.tf1".i;"1 statri i i t ' of the vcssl,t ar anr. arrglc of hcei i.c. lhc\ \ , , rK_ d { r j r r i r r i nc l rn ing the res

l, utrl .rs rire p."rr.,-"i ' i i

" ' l iel-,uPk)

that '1ngle (This can bc.,."o ,.,,'J". ,r,"'.uil'J'.,:ll:"i:ll]ff;ll"ii,jt,,,'ii "lil::, ,i,ll",:li:

\ \ ' h ' 1 J 1 1 1 s h c \ l ) i l 1 J q t r i l \ t h L , \ . .ihe, code or ;,,,j., .,,"i,,ii,,1.-,,,.":l:::.:"iirJ:.. crircrh speciricrl in

,\ccul' l tc !1.t(f lnrnntion or List producecl clue io transvcl.se shift ()if lrr ' .trp s .rntre oi. Cra\ riv, or clue to , f,r*f i"g--,"",;ri

";f1,,.f .

i l l;, ' ';"t'" of loll in 'r 'esscl 1r'rrh arr inirrar neSarive ,,'eLrccDrric

,tr()ugtr, theoreticall! t lrc shiPs C\l (f luirl) can bc founel htrnrr _Lur\

( , r t j t . r t lc.r i sf . rLrt l t t \ d!

_ ii,,,:: n"ul*',:ilrtlli- :i: ii['"'.iiT"i]li :ilt:;'."':, i:,i" ",0:::;i:,';ll

"l;t",1'l;,li ;i: "'.;l}ll; s',,, l":,'^:l

[ ]

t .

2.

3 .

.1.

:|

o.

INTACT STABILITY CRITERIA FOR ALL PASSENGER ANDCARGO SHIPS

Thc arca under the CZ curye shoulcl not bc lcss than 0.055 rneicrraclians upto an angle of heel of 30'.

The area under the cun'e upto an anglc of -10" or the anglc oif looti ing (rvhichever is least) shall not be lcss than ().09 metcr raLlians

The area urrcler tlle curve betu,een 30" ancl 40" or the anglc of flooLling(rvhichcler is least) shall not be less ihan {).03 Irreter-radians.

Thc righting lcvcr GZ shall bc at l! 'ast 0.20 m at an angle ofhccl cqual lo or greater than 300.

Thc maxirrum righting lcver sht ul,. l occur rt arr rngie tri htclpreicrablv cxceeeli:1g 3()'r Lrut irol less thau 25'.

The inii ial metacentric height should not bc lcss than {).15 m.

ProYision shall bc made for a safe margin of stalri i i tv at all stagr:of t irc vovagc, rcgard bcing given to additiorl of \\ 'eight, such a.thcsc cluc to nbsorption of u.atcr and icing and to loss of lvcightsuch as thosc due to consumption of iucl .rnci storcs.

Ships carrving oil-bascd pollutants in bulk, should be able to satj\ lthc abo!e criteria cluring all loading and ballasting opcrations.

In arldit ion, ior passenger ships

(i) thc angle of hccl on account of crowdi|rg oi Passengcrs rone sicle shoulcl not exceei-l l0(', and

(ii) the allgle of heel on account of turning should not exceer:-l0L' rvherl calculatecl usirlg ihc formula:

, , - v, , : . . f -_ dlp1.. = 0.02 r xW KC, L \ 2 )

nrhere M, = heeling moment (mt)

V,, = service speed (m/s)

L = length of ship al $'ater l ine 0n)

W = ciisplacement (t)

d = draft (m)

| 1

KG = that

'-\issengcr and cargo:rg criterion (l 'eather

:'f ship b lrithstancl

of ship (m)

ships sl.rould also satisfY the Scvcrccritcrion). This criteriolt indicatcsthc combined effcct of u'incl ancl

ltincl anrlthe abil itYroll ing.

l l 5

SHIPS CARRYING TIMBER DECK CARGO AND USING TIMBERLOAD LINES

For ships carrving timber deck cargocs and using timber load l ines, Pro!id".:ihat the cargo extends longituclinally betn'cen suPerstructures (if ther. -

no superstructure at the after end, the timbcr deck cargo shoull i extcijto thc aftcr cnd of the after most hatchu'ay) ancl transverselY for the f.:beam of the ship, thc Administration may aPPlv the follolving critc:::in l icu of those mentioned abovc for cargo ships.

1. ' lhe

aLca unclcr the GZ curve should not be less than 0.08 n1.:.:radians upto an angle of ;10" or the anglc of f lootl ing (rvhiche .:is least).

' t1 . . . r ioh t i - ' l ' . \ c r s l r , 'u l . l bL ' J t l c . r ' t ( l 2 . In

3. lrr thc eleparture condition. thc metacentric height shoulcl not Lre l! ' : ithan 0.10 m anel at all t imes .luring the vovagc thc mctaccnt: -height should bc positive aftet correctiol for F.S.Ij., absorPtion .u'ater bv the cleck cargo and accretion oI icc on exposed snrirc.-

SHIPS CARRYING GRAIN IN BULK

(As Per Grain Code)

l

)

l .

L

Ships carrr,ing grain in bulk should satisfi thc follon'ing critt ' :.:throughout thc vovage.

Thc anglc of heel due to the assunecl shift of grain, obtaincd :plotting the hecling arm cu'e o'Jer her cun'e of sLatical stabrl::ihall not be grcate'r than 12r. ln ships constructed on or atter l-:

January, 199-1, the angle of heel shali not bc grcaler than 12thc angle of heel at which thc deck erige immcrscs, u,hichcr.:is lcast.

The residual positive area betrvecn the heeiing arm cun'e ancl ::-curve of GZ upto an angle of hecl of 400 or the angle of f loorlr. :or the anglc of maximurn separatioll betwecn thc hcclir-rg atn cu: -anrl the CZ curve (r'hichever is lcast) shall not bc lcss than L)r-:mcter radians.

The initial GM (Fluid) shail not bc lcss than 0.3 m

ship shall be upright on proccccling to sea.l he

i f requircd, bcfore loading grain, the mastcr shall

l : 11, : f : "1 ' l l * . r loacl ing co| 'J i r rorr . the .h ip $ j l t\ - f l t ( n . r , l l . r J J s t 1 9 , . , , , r i / r e r n r a g e .

clenonstrate thatmcct thc abo\.e

) . 1 ,

ArsumcJ volu metric hcelrn* momentSto.w,age factor

.7'n x 0.8

x displacenent

: offshore -supplv vessels of not more than 100 rn in length, r,hercrcsscls cha.acteristics render compliance *ltfr tn".rjt".io'uor".a.iLr".r

..,iiso .tilt lnpraciicabte, the e.tniin;stiation",ruu-oppi.,:'ii" tr,rtr,r*,;,'g

,l-T:*'l: l l righting lever shoutcl occur at an angle of ncer nortess than 15'l

The area untler the GZ culraclians upto an angle of 15.,-::": l. ' : ] ' l

not.be less tharl 0070 meter-at 15.

when the naximum righting lcvcr occurs

'iroulcl not be less than 0.055 meter- radian upto an angie of 3(l rvhcnj,.J]]-1i'l*- righring Iever occurs at 300 n. nLro.rr.

..wfr"i?'an.] nl,nr,-u,.::::urg lever occurs at angles bet$,een 15, o"d 30; t i]" ..r,r"rp""Or.g: uncler the righting lever curve should U" ut t"uri

t

OFF-SHORE SUPPLY VESSELS

[ 7

.1.

0.055 + 0.001 (300 - e,"",) meter-radians.

The area under the GZ curve between thc angles of 300 and 40or thc angle of flooding whichever is least shoulcl not be less than0.03 meter radians.

a. Jhe fighting leler (GZ) should be at least 0.20 m at an angle ofheel equal to or greater than 300.

5. The initial transvc'rse metacentric height should not be less than 0.15m at ar angle of heel equal to or greater than 300.

Compliance with the stabil itv critcria does not ensure immunitv .lgainstcapsizing regarclless of the circumstanccs. prudence ,rrrcl good seamanshrFshoulcl be exercisecl having regard to the season, &,cather anJ the r-ravigationaizone and appropriate action should be taken as to course anci spccd warrantedbv prevailing circumstances_

The sludents's attention is drawn to items 7 and 8 of theWhen cletermining GZ values from KN, the correctcclto be used.

Gencral lnstructionsKC (KG - FSC) ts

DETERMINATION OF LISTFROM CURVE

DUE TO TRANSVERSE SHIFT OF 'G'

OF STATICAL STABILITY.

The student is alreadl' aware that the l ist Produced bv a transverse shrtt, ' f e can bc obtain,... l bt the c\prcssion

,." " = cg.

' ' " " - c tv t '

provicled tl-re list is small. The reason whv this exPression is not aPPlicablcat large angles of heel is that as the l ist becomes largcr, the valrre oiKN,l and, lherefore, GM changes considerablr' (as her $'ater plane arcn ch.rngc<rvith hecl) and tl.tus the initial GM uscd in the above expressiou is n,,mole applicablc. lhe list mar', howcvcr, be determincel accuratelv fronla curve of statical stabil ity as explained below.

r {.1

. loacling, discharging or shift ing operation mav produce both a vertical:: and a tiansvcrse shift of G. As clone in thc previous problems.urvcs of staticai stabil itt, the CZs at various angles of hecl n'ere

. :rtrl, bv the cxpression GZ : KN - (KG sin 0). The KC used in- .\pression is the final corrcctecl KG obtainecl after aliou'ing for anv

. l ' h r l l o l C , rn r l . r l \o rhv fqc .

-:f a transvcrse shift of G is also involr'cd, it can be sccn from the. on the pre\' ious pagc that the GZ at ar-r-r anglc of heel, on the

tr rvhich shc is heeled, rcciuces [ 'ry an amount GG, cos 0.

-.i. i i11 thL' l isi fLom a curvc of statical stabil ity the final KG (corr.ecterl:: l irst oLrtained, arcl ihc GZ valucs at the \ 'arious angles of hecl

-r.:tcrnrinecl bY thc cxpression GZ = KN - KG sin 0. lhe reductionI due to transYcrse shii i of G, equal to GG, cos 0 is then subtrncted:hc CZ values as obtainccl abo\'e. Thc corrected CZ values so obtainccl

: ' .(,ttcd as.1 curvc of statical st.tbil i t\ ' .

:ii ls then rcacl off, rvhere the cutve attains zeto \'aluc, as .it earlieri thr' \ 'essel has a -\ 'e GZ (heeling lcver) ri, 'hi le at larger anglcs,'.r i +\'. CZ values (Righting levers), as can be seen from the currcs

::-r iollo\\ ' ing problcms.

rl! l bc noted that the curve drarvn is onlv Ior the side b uttich- irstcci. Though thc GZ l 'alues .irc negati\c inrtiall\, jr is imFortant:. ' that this is not due to a -ve CM. As the C shifts translersel\ ',-!\cl l ists ti l l lhc new Centre of Buo\.ancl once again colncs in thc, eri i.. i l l inc as the centrc oI Ctavitr '. At this l ist, she attains statrc

-'ri u 111.

I 4 5

DETERMINATION OF LIST WHEN GZ VALUES ARE GIVEN.

In a theoretical problem where onlv GZare givtn, !1 hereafter some vertical anllthe GZ values for the new condition

1. Acid or subtract vertical GG, sin

va lues a t J i f fe ren t ang les o f hc<.transverse shift of C has occurredmal' be obtained as follows:

CC

0 (+) for downwar.l shift of(-) for upward shift of

2. Subtfact hansverse GG, cos 0.

The statical stabil it) 'curve mav now be plottecl and the l ist determine;as inclicated earlier.

This methocl is resorted lo as KN and KG valucs areto use the methocl indicated earlier.

CURVES SHOWING MINIMUM INITIAL 'GM' REQUIRED(OR MAXIMUM KG ALLOWABLE) TO COMPLY WITHTHE MINIMUM STABILITY REQUIREMENTS OF THE

CODE ON INTACT STABILITY

- :. curves are proYicled as a part of the Trin & stabil itv particul;rrs.hips. From the last proLrlcm, the student $,i11 appreciatc that therl. it ions involvcd in ensuring tl. lat the vcsscl s.tt isfics thc lnllrnlurrl

' :,r iv requirements, is rathcr t imc consuning Separatc curves indicatingirl inilnum CM or ntaximum KG w.hich ivoulcl satisfv cach of thc;rum siabil itv criteria arc devcJ,rpggl rn ihc.hipJarLi .rnd ploticd with: displacemcnt on onc axis ancl the minimun GNI, or marimum KG:he othcr axis as shon'n ir the diagram at the encl of this text.

:.rn L-rc secn from the set of curves, if t l-re ship's CN,l is gfcater t i1.tn'i lucs r-eprcsented br'cach curr'e, the ship $'oulcl satisf\ ' .t l l the i lurrntullrr, itv rcquirement:;. Thercforc, i i is cvident that, all thc rcquirelncnts*rtrsficel proviclccl thc GM laluc at i lnt particular clraft/rl isplaccnrcnt

:rf, lter than fhe ralucs rePrcscntcd b\' the tlottccl cnYeloping l int. This'nrntion is proliclecl as curves or tablcs of minimum GNf, or nraxrnrunr.,r ' rnaximurn cle,rducight mornent reiaied to clisplaccment or clraft in

:...r1(.r. lf using the clcac|.r 'eight nroment, the frec surf.rce Inontct.tt L,t' irrP 5h6uld bc aLided to the ship's dearlncight norrcnt bcfore crrmprrisLrr

.. hcr nlaximurr pcrmissiblc rlcactveight momL,nt for thai cljsplaccntent.

. iqlr i i rvoulci airpcar frotn thc abot L', that GNI is thc onl\ ' par-antetol--r con:j ir lcrecl regarding the ships stabil it\ ' , thc student shoulcl realizc

Gi\1 r'alues rcquired to s.lt isf\ cach stabil itv rerluiremcnt, have bcctl,.rfreLl Llsll19 thc Ininimun .riteria as regarcis st.tt ic.l slabil it] ' curvcs.ir)rLlarrcntal irrPortance oi thc statical stabil itv curvc fot. ar-rv condjtjorl

: l(1 r)ot thcrcfore Lrc cvcr rrnclcrrrtrLl As .r critLri()n ol l iel stabil it l' surl ivnl capabil it\ in a sent{at, hcr cun c of siatic.rl stabij it\ ' , thL,' untler it antl hcr GZ valucs at vaiious angles of hccl are of uhlost

',rtance. lhis is so bc'causc thc areas undcr hcr st.tt ic;t l stabil itt curre,.-i l arc functions of hcr clr 'n.tmical \t.rLrl l i t\ i t th,rst . lr 'r,r1"r t,f hetl shouLLl,rr{o errough to ovcrcornc an! hccling momcnt applic.l to thc shiI\ 'a\cs, \\ ind L'tc. uncler even thc \r 'orst weather anci sLitc of sea s]te

.:rt 'h kl crpcriencc cltrring thc vovage.

:\ requirccl to nrcct stabil itv critcria prcscriLred for her class nI vtsselsr in a dnmagcd condition arc proyiciccl \rith curYes of taltcs oI mjnrnrnnr

:or rri l \ imLtm KG to be maintaincrl in the ini.rct condition, so that,-:rtL' thc assu111cd ciamage for hcr ciass of vcsscls, she rvjl l ncct thr.::..rgc stabil itJ critcria for hcr class oI r 'csscls.

ships officcr shoulri bc' a\\ 'arc th.rt thc KN,t arailablc to him ur rne

r 5 l

"Hvdrostatic particulars" of the ship, is for the UPRICHT CONDITIO\ln most ships, as in thc case of M.V. 'Hinciship', thc KNI Providecl, t.for the EVEN KEEL CONDITION. Should the vessel bc trimmccl, thishapc of hcr waierplane u'i l l change causing a corresponciing ch.rngc i:thc KNI, and iherefoie in the GM. This cffect wil l be verv pronouncerlin casc of ships lvith fine l ines. As the aftcr nater plane is consitleratri.fuller than thc forward onc at certain drafts, the CM is l ikclv k) rcduc.cor-rsirleraLTlr', \\4ren trimmeci bv the hcad.

Sor.nc ships nlav be provided $'ith important hvdrostatic particulars fo:cliffcrcnt trinrs. Whcrc such particulars are available, the ship's oilrce:should uti i ize the Llata for thc actual trim the ship is in, as this \\ 'r l .ploYicle hirn u'ith more realistic results. Hou'evcr, if thc ht t lrostatic particularsof his ship are available onlv for the Evcn kecl condition, he would.iol 'ell, to ensure that thc calculatcd GNl, of the vessel is large enoughto allow for anv change in the KM, causcd cluc to the trin.

lVhcn the ship is at sea, ancl pitching hcavilv, the change in KM rli lbe verv pronounced, particularlv in ships with finc l incs. In such shipsif thc GM js not adequate, it maY be noticed, that rvhcn pitchccl hcavil ithc CM may' bccomc vcry small, or cvcn negative, lhereb-\' causirlg th.ship, to roll to large angles.

Similarlr ' , lvhen a vcssel is ro1ling, hcr I-CB changes as her angle of rolichanges. lVhen the LCB changes, her trim altcrs. This is knorvn as frectrimming. This cffcct is vcrv promincnt in small ships l ike offshore <upplrvesscls anci to a lesscr c\tant ir1 larger ships. The Cross Cur\'cs of stabil it\arc thereforc no$' rcquirccl to bc providctl to ships on a free trimminqbasis for a range of clisplacements between light and load clrafts anci arange of trims anticipated in normal operating conditions. (Rcfcr to stabil it\information to be provided lo ships on page 1.)

1 5 8

Il\.41N MUI',4 6M REOUIRED TO COMPLyWITH CODE ON TNTACT

STAB LITYFORCARGO SHIPS

I t 9

CURVES SHOWNG THE MINIMUM INITIAL GM REQUIRED TOCOMPLY WITH THE STABILITY CRITERIA AS PER CODE OF INTACTSTABILITY FOR CARGO SHIPS

The curves A to F on thc previous page shon' the minimum GNl requircllat dif ierent drafts to comply with each of the Intact Stabil itv Code rcquirementsas inclicatccl belou'.

A) Arca under GZ curve upto 300 shall not be less than 0.055 meter-radians.

B) Area under GZ curve upto.l00or the angle of f looding (whicher e:is least) shall not be less than 0.090 meter-radians.

C) Area uncler CZ curve bctwcen 300 & 400 or angle of flooding (whicher e:is least) shall not be less than 0.030 mcter-radians.

D) That the Righting Lever (GZ) shall not bc less than 0.2 m at ::a:rgle of heel or equal to or greater than 30".

E) The Maximum Righting Lever shall occur at an anglc hccl of r :less than 25'r.

Tlic Init ial Metacentric Hcight (CM) shall not be less than 0.15{l:-

The dolted enveloping l ine indicates the GM required to cornF..with the cntire stability Criteria (A) to (F).

F)

c)

t 6 0

DRY DOCKING

,j1cn a ship is f loating, thc weight of thc ship is balancecl bv thc buulancv. rJc t l bv the unJerw. l te r ro lL tmu. fh rs nou l t l be , " , . rcn , i t th .'r i. lnt \rhen onc encl of thc ship just touches the blocks. If the u,ater

.,1 falls lhcreaftcr, a part of the weight of the ship rests on thc blocks,:rlc the rcmaindcr is supportcd bv the buovancy providccl bv the retluced-,rcr\4'atcr volume. Thus, at any instant the total weight is balancecl

1i)t l.re upu'ard reaction from the block on thc keei iwhich is equalrrright of the ship resting on the blocks) and (i i) the buovanc,

:rg pIo!idccl bv the reducecl underwatcr volume

reaction provided bv thc blocks acting uph,arcls on the kcel mav:,rrrsiclcred as a negatiYc wcight, or a u,erght discharged frorn that

.'.: Thc sturlent is alreacly a$'are tltat when a weight is ciischargetl,w . t l

r t ' r ' t ical CGr h,hcre 'd' is the vcrtical distancc betu,cen G

:hc ship and g of the $,eight dischargcd.

:. if the reaction provicled bv thc blocks is,p,tonnes, the virtual nsc:rr. ships centre of gravitv (GGr) or in other $,ords, the !irtual loss

PXKG. CNl, r.rn b( obtaincJ br the t.rpre.sion, W.P , rvhcre P thc upthrust

:,lccl b1' the blocks rnav considereLl as the $.eiqht liischarseLl. and::.,e vertical distance between the ship,s G and the g;f \\,urghr .l ischargccl:rralent to'ci ' , as in this case, the ncight has been considcied dischar[cci- tho kecl levcl. The KG to be used in this expression is tho KC:hc KC correctcd for FSC). This virtual loss in thc GM mav also

PxKM'uttd by the cxpression CC, =

-. KM for the virtual displaccment of:or a displacement of (W p).

, whcre thc KM to be used

the vcssel at that instant i.e.

w-P

' though thc loss in GM and therefore the residual GM calculatccl separatci '

usingl the trvo expression $'oulcl give slightly dilferent rcsults, it shoul':

not "bc

inferrcd that ihe slight clifferencc is due to one exPression beini

rnore accuratc than the othcr' This is tiuc to the fact that the criteri(':

of the ships stabil itv is the Righting Moment she has at an-v angle r:

hecl and not just t'he initial GM Thc Righting Moment obtaincd f'-:

anv snall angle of heel bY the expression W 1 GII'I sin 0 utilizing ll- '

GNI obtainecl lv eithcr of the expressions u'ould bc nearlv the salre Th:'

is so, bccause in onc case the virtual disPlacement of the vesscl is r'"'

- P), u,hile in the othcr case, it is W itself.

It is essential that the shiP is stable at all stages belrvecn the first e::

of thc ship taking blocks and the entire keel resting on thc blocks' O:::

thc cntire kcel takcs the blocks, the stabil ity of the ship, is not a ma::':

of qrcat conccrn. Horl 'evet, rvhen onlt ' onc end of the vcssel is rest:: i

on ihe blocks. should she becone unstable, shc u'i l i heel over, Llalnat -:

her bottom ancl the blocks. To ensure that she is stable throughout :=

period between one end touching the blocks and the entire kecl res:r::

on the blocks, it is sufficient to ensure that she is stable at thc rns::::

bcfore thc second end of the ship takes the blocks lt is obvious r':1

ii she is stablc at that instant when the second end of thc shiP ta'=

the blocks, she nust have been stable at all prior occasions for the reai -

that as the ievcl of !\'ater falls the force P increase ancl thcrefore :-t

rrrtual CNI ol tht' vesscl . lecrease' throuthnut this PerloJ

Lhe FSC, when a Part of the ship's weight is taken on the blocks is

FSM

-lo calculate the loss of GM at the instant, she takcs the blocks all c --:

it is ncccssary to kno$' the value of the force P at that insiant ::-s

can be easilv obtained as the totai trim she had on entering the 'l -cr'

is nullified when her entire keel rests on level blocks The trim::::g

noment that she hacl on entering the tlock is cqual to trim in cnr' :

x NICTC. To reducc that trim to zeto, an cclual and oPPosite trtnl:':

moment $'as provided bv the uP$'ard force P acting at the end o: :-t

ship rvhich fir it took the blocks. The trimming moment Pr(Nided br:--r

force = The lorce x its {ore and aIt distance from tl-te CF.

the initial trimming m.:force 'P' rvoulcl be equa-

and aft distance betu'eer :

CF and the end of the ship *'hich took the block lirst ln the :-'

expression, P is the onlY unknown, which can be deternlined an'i :l

used ir-r thc expressions mcntioned earlier, to ascertain the virtua'

Since the trim has been recluced to zero,ancl the trirnming moment Provided by theP x a - t x MCTC rt 'here'a is the fore

of GM at that instant.

l 6 l

'r:tcr she takes the blocks ali over,: r:ierence bctween her displacement,:i( i i l lat at her present hydrostatic'c vcssel has taken blocks all over,

':.r it would all bc the same.

the force P can be obtained as lheat her hydrostatic draft rvhen afloatdraft. If the blocks are lcvel ancl

the picsent draft F, A ancl hvdrostatic

\ote: L)uring clrydocking, thc virtual displacement, KM, MCTC, LCF anclFSC of thc vessel u'ould ch.rnge with the tall in water level. Fora small change in the draft, the change in the above parametersij, ni 't qigIl if icanf antl thercfore rnat be disrce.rr,led.For a

not be

large changc in draft, the change in these parametcrs can

FSiVrgnorecl. Also. the FSC then is W_P

r ressel \\,ith an initial ncgative metacentric height is unstable in the upright'nditio11 and therefore heels oyer as she has a capsizing lcver lvhen inclincd- rqhtl\'. On hecling, thc centre of buoyancy moves out from the ccnh.e

re iill, at a particular anglc of hcel the centre of buovanq, ancl the:ntre of gravity arc in the samc vertical l ine. At this angle of heel,:,: C ancl N{ are coincident. 1hc angle of heei at lthich this occurs- called the angle of loll. In sti l l naier, the vesscl rvil l rem:in heelcci

that anglc. it shouid be realisec.l that no rightin€i levers are present,-. io the angle of loli on cither pori or starboard sii les. . l.hus

she mav-.-lLnc to her anglc of loll either to port siclc or to starboard srcle.-o!gh she attains positive stabil itv and therefore righting lcvers at largcr'q1es of hcel, u'her.r rolling in a scau,a\,, it shoulci be rcalized that theihling lel 'ers rvould be tairly small as her starical stabil it\ cur\c is shalloq,.

: .-n a small heeling moment r-r,ill thcrefore cause the \uessel to hccl ovcrdangerously large ang]cs, bccause her dynamical stabilit\, (\a,l1ich is a

.::rction of the area under the positive pait of the curve) is \.ert, sntall.

ANGLE OF LOLL

': iollowing sketch i l lustrates the statical. ' .1 and of t ltc samc vessel with init ial

-.an be seen from the sketch, the vessel:hl has capsizing levers till her angle ofangle of vanishing stability, the range of

:- ' i irty at any angle of heel are all very*: r 'cssel with +ve GM.

curve of a vcssel i\.ith a +\'c-\'e GM.

with an initial -ve metacentricIoll. The maximum GZ value,+ve stabilig and the dynamicalmuch less than those for the

t 1 7

Should a vessel devclop a -ve CM, at sea, due to unloreseen crrcumstance's

it should be rcalised that she u'ill roll to very large angles of heel and

not just bctween the anglc of loll on either side. This is so bccausc

as she rolls fron-r one side to the other, since there are no riShtir'\g levcr\

operating betlveen the anglcs of loll on either side to oPPose the roll

she builds up a large amount of rotational energ,v. Since her statical

stabilitv curve is shallot', the area under that curve and, therefore, the

dvnamical stability upto anv angle of heel is ver,v small Thc- rotationa:

encrgv cannot therelore be overcome till very large angles of hcel art

reached. This can result in shilt of cargo causing Iurther dctenoratlo'

in the situation, possibiy leaciing to caPsizing

To corect such a condition, it is necessar,v to remcd)' thc basi' c'ru"

i.e. G being too high. The G mav be lowered bv reducing frcc suriacc

effect in various tanks or bv trimming down wcigl1ts or bY ballastin:

at a low level.

When ballasting, carc should be taken to ballast a centrc iank of sn1'r'

width (to reduce FSC during ballasting), ancl if that is not available, ;

diviclcd tank, commencing u'ith the low sidc. When that tank is iu:'

the high side tank should bc {illed to even out the t'eight clistriblrtio-If on the contrary thc high side tank $'as ballasted initialll', as rrou,;

hale been done to cottect a list due to excess u'eight on the loh'sidi

it uoulcl lead to Llangerous conscqucnces including capsizing- T}is cou!:

happer.r because, on aciciing u'eight on the high side, she u'oulcl f lol '61"

to that side and heel further to dangeroush' large angles on that sit l '

or e\'en caPsize.

The stuclent is alreadv familiar i l i th the drau'ing of the cur"cs of static:

stabil it l for anv conclit ion. The angle oI loll can be accuratelt ' cletcrmin.:

bV clral{ ' ing thc statical Stabil it l Cun'e for thc conclit ion she i\ in ir j

then reacling of1 the angle of 1o11 from thc curve at the lroint at \'\'hi':

the righting lever becomes +r'e.

An approximate valuc of the anglc of loil maY be obtained quickll ' , prorio.:

the angle of lo11 is not large, assuming the ship to be rvallsiclecl, :

the use of thc exPressioll:

l2cN4tan c = !_

lol l, she clevelops positiveioll ma1' be obtained bY

At the angleat the angle

ofot

stabilitt'. The positive Gi.1the expression:

2 x initial CM x sec. angle of loll

l l l t

Thc ships KC for anl' loading conclit ion can be calculated, provicled itslalue is knor.r'n accuratelv for the l ight conditiol). Light ship means theship complete in all respccts but u'ithout stores, consuinables, cargrr, crc\\,and effecls and without anv l icluids except that machinc!\, and pipingfluids such as lubricants a;d hvdraulics ire at operating levels.

Regulatitrns II - I/22 ot SOLAS requires evcrv passenger ship regardlessof sizc and cvery cargo ship of lcngth 24 m and oi,er to be inclinerlt() clcterminc the clements of her stabilitr'. l{hcre ant, structural alterationsare maclc to the ship thereaftcr, h'hich rvoulcl affect l-rer stabilitV elcmcnts,- r r , J r ip s l r . r l l bL re - in ( l inc ( | .

At intervals not exceecling five vcars, a l ight wcight survcv shall be carricclout on^all passcnger ships to vcrifv anY charlge in l ight ship ciisplaccmentantl l,CG. If thcrc is a cie\' iation of l ight -ship rl isplacement crceccling2oi, or a cicviation in thc LCG cxceeding 19i of L, shc shall bc rc_irrclinctl.

Ihc aciministration mal ailo$' the inclining test to be c.i ispensetl n,ith foran inciividual ship prtvided basic stabil itv c.lata arc avii lablc from thcrnclining tcst of a sistcr ship. The Admjnistration m.rr al: jo .t l lol| thcrnclining test to be clispenscci \.r ith for an intl ividual ihip or class ofihips spccialh ciesignccl for the carriagc of l iquicls or oie ir.r bulk, ifi \\ ' icfcrence to existing data for similar ships, it clcarly indicates that.iuc io ihc shjps proportions and auangcments, more than sufficient:nL.tacentri€ hcight wil l be availablc in al1 probable loacling conciit ions.

,hc inclining tcst is carried out in the ship \.arcl, u,hen thc shrp ls as:cnr col]1pletion as possible.

. rlo or three long pcn{sls65 are gencrally rigged, one fonvard, onc mirls}rips:nr1 one aft. Thc pendulums arc of pianou,ire, anc.l their bobs arc immersecj:r iroughs of oil to rlamp their oscil iation. The pcnciulums shoulrl bc

.i i.out '1 to 6 m in length anrl shouic1 gir.e a cleficction of at least 15:rrs, r\hen thc ship inclincs. The use of three pendulums arc Lecomncnclctl- 'Lri a mininum of two should be usccl. Thev shoulcl bc located asr-1r apart as practicable ancl should be protcctej i lom h,rnrl Thc use: an inclinonctcr or U tube mav bc consiclered. Therc should honcvcr-r at_lcast orc penclulum. Gradu.rfed b.tttens al.e set up bene.rth cach-rldulum to measure the clefiections of the pendulum q.hcn the Ycssel. c ls .

INCLINING TEST

:rallr ' , six cqual weights are placcd on eleck,- Lral clistanccs off the centre l inc. Thc:st' l shoulcl Lrc such that whcn the! are

three on cach sidc, at ncasuredweights usecl for inclining tlrc

shiftecl translcrsclt, ther rvil l

l l l l

proLluce an inclination bet$'een 2 degrec and '1 dcgrees ln large shipsa minimum inclination of 1 dcgree mav bc acceptecl lf the inclinatiorproducccl is too largc, her $'ater Planc area ancl thcrefore her KM willchangc significantly ancl the inclinatiol-t produced rt ' i l l not be Prolrortlonalto the inclining moment provided- C)n thc other hanci, if thc inclinaiionis r,ery small, an\r small error in reading thc deflection on the Plumbline rvoulci introcluce significant errors in the calculation of hcr GM

The init ial position of t l.re plumblinc is noled a€lainst each battcn Usjnga clock sielc crane, one $,'cight is shifted port to starboard anci thc eleflectionnoted on cacir plulnbline. A sccond weight is shifted Port to starLro.rrdanrl the cleflectiorr on the plumblines notccl again. Thc third weight isnlso tl-rc'n shifte.i port to starlroard and thc cleflection of cach plumblincnotcd. All the threc shiftecl rveights arc thcn relurned to thcir original

l.rosit ion on thc port side and the deflection, if any, on the plumblinesnoted. This entire procedure is then rePcated $'ith the thrcc lveightsfroln thc slarboard side. A plot is then made with the heeling moment (r\r d) orr thc X axis and tan 0 (dcflcction / length of Plumbline) on theY axis. Thc plot of all readings on each penclulum should l ie on :straight l ine. Deliations of anv plot {rom thc straight l ine indicates tircrcrverc othcr monents acting on thc ship during that inclining. These momentrshould be icientified and rcmoved and those rreight novements r\jFcatecuntil a stiaight l ine of all thc plots is achievecl.

I]EFI-ECTION OF PLUMBLINE LINE

LENGTH OF PI-UN,IB LINEL\N 0 =

1 8 2

.. hcn a lveight of , iv, tonnes is shiftecl transversclv through a clistance

metres, thc l isting moment = d x $,tm ancl the. l ^ \ v

tr.rns\ Lrse CC, = U,

rn

Or GM c(alV . tane

c i 'u '

cteilectionicngth of plumbline

.hould be notccl that 'W, usccl in thc calculation is:hL'ship at the time of the inclining test, incluciing the

-i .rnY other rlcights on boarcl. The CM obtained. . .1 ) o f t l r . * l l l p rn rh . r t .onL l i t ion .

. KV for displacemcnt 'W' t is obtaincd from the Yesscls hvclrostatrc:.r B\' subtracting the calculated GM (Fluict) from the KM, *" oo,ou1- .orrectccl KG in that condition. The FSC if ant, is subtracted froDr

corrected KG to obtain her KG rn that con(ilt ion. B_\ tali l tg nlomentsrt thc keel, allo$'ance is then madc for an_,,. weights on hoar.i] rncluclinginclining.w'eights, nhich do not form pa;t of ihe l ight ship, to oota:n

: i jght KG'.

':(autions ne.essary when conducting the Inclining Test.

The ship must

The ship s trimtrtnl cl()cs not

be upright at the

should be such thate\ceed 1"; oi I_.

l l l l

thc dispiacemcntinclining rvcigirtsrri l l be the CM

commencement of the test.

the deviation from her clcsigncci

3. I-Ierher

draft should be such that abrupt changes $'ill not occur ::water plane, when inclined.

An accurate list is to be maclc of anv itcms of lveight vet to :':placecl on board. ancl thosc to be temovcd fron1 the shiP, togethi:u,ith theil KGs and LCGs so that correct allo\\'ance can bc mac=for them in the calculation of the ship's light KC an.l LCG.

TemporarY material, tool boxes, staging. sand, dcbris etc. on boa:-should bc rcmoved and all personnel not involved in the incLini::test should also be scnt ashore.

Decks should bc free of water ancl sno\v or icc should be rcmor'.:

Plcfcrabll, all tanks shoulcl be empq' and clean or comPleteh fJSlack tanks should be kcpt to a minimum, their exact sounelir.:.noted and thcir FSC accuratel)- clctcnnined, to allou' {or the $'eis.:of liquicl in them and iheir FSCS in thc calculation of light sf :

Pafameters.The ship should be moored in a quict, sheltered area, free ir.::external forccs such as propcllcr wash from passing ships ol discha::.from shore sidc pumps.

Ideall1', there should be no wincl, cuttent or tide runninEi.

The depth of water should be sufficieni to ensure that she 1 ..not contact thc bottom at an)' location, u'hcn inclined.

Thc ship should bc so moored as to allow unrcstricted heel.iAccess ramps shoulcl be removed and polver lincs hoses etc conncc:-:to shore should be minimizecl

A11 derlicks, boats etc. should be housed and securecl in their seago:::condition.

The clraJts, F, A and midships should be accurately read on e:.--siclc of the slip to establish her u'ater linc to determine hcr displacemt::accuratcll', at that time. Thc sPecific gravitv of theu'ater sho-.:be obtained accufately by taking water samPles forwarcl, midsh:-ancl aft, at a sulficient depth.

The test u'eights used should be aon.rpact such that their VCGs i--be accuratelv dctermined. Their weights should be accuratelv lecord.-:

Water ballast transfer is generally not accePtable, for inclining the sl-::

f ,

6.

7 .

8 .

9 .

10 .

11 .

12

15.

14

1 8 4

DRAFT SURVEYS

ri thc lessel s loacled displacemcnt is obtained and the sum of the light.1ispl;rcement, 'constant, ancl weight of other non cargo iteits on boarcl-rre subtractcd from the load displacement, ihe $,eight of cargo on board.hould theoreticalh' result. Hoi/\rever, this methocl ii subject to errors duc:o thc unkno$,n quantities such as u,eight of bottom tnuti,.,!, nr.rJ-tf,"

""o.t:.cight of thc constant etc.

__ Alternatively, the quantitv of cargo loadecl may bc estimatecl as theirlterencc i i displacencnt before .rnd after Jo.rding, aiter rnali[g a]lorvancc

:,r-. knol\'n non-cargo items on board such as fueJ, storcs, fresh'r,r,ater, anv-.rllast etc. at both ir.lstanccs. Similarly, the quantity of cargo discharg,-d

]l o:::1^"** hv comp:rjng the displacemenis before and itcr dischaigc

ter m.rKmg alior^ ancu 1or the r.eight of non_cargo items on boarcl at-'th instances. This n-rethod u,oulcl be preferable 'as

unknc,wn quanuues-::.h as rvejght of the ships constant thc neigl.rt of bottom fouiing etc.. automatically allowed for in this nethod as they would add to thc::iplaccment equaliy at both i istanccs. 81, using the same procedure at

r Joading .and dischatging port5, the results ca'n be cnmpared ancl any' r r r i l l ' hou up .

I,\rhen conclucting a draft sun ey, the drafts F, A ancl mitlships shoulclreaci accurately, on both sides t,f thc ship, to obrain thc rneair oI p&S

::rts F, A and an-riclships.

--rrrection for Position of Draft Marks

. ships hr.drostatic data, including her clisplacemcnt scale are provided: drafts measured at the fore ancl

_after pcipendiculars, at her ilesigned::r. u.ith no hog or sag. Since the p & a draft marks mav not behe perpendiculars and similarly the amidship draft marks not exacth.ne mid point.of the. length. bctween pcrpenilicular (where the plirnsJl,:is are exactll located), the observecl clrafts should be corrccted to obtaindrafts. at the F anc-i. A. pcrpendiculars antl at the mid point of thc': ih betu'een perpendiculars.

l 9 i

Fol the casc illustrated above, thc lcngth betlveen end dra{t marks = (LBP- a + b), Ior rvhich the trim (observed dralt A - obscrvecl dlaft F) i.

t corn. F cornsav ' im. Thcn bv proportion,

Thc colrection io thc observed clra{ts are thus obtainecl and '"r'her-r tirescare appliccl to the obscrved clrafts, wc obtain the drafts at thc F&:perpencliculars ancl at rnid length. An inspection of the plan w'oulcl intlical,'rvhether thc corrections arc to be addecl to or subtracted {rom the obsen e.:clrafts. ln the casc illuslratecl, thc corrections arc to be subtractecl t('rthe obscrlccl dra{ts F and A and acltlecl to the observed draft alnidshrp'

Correction for Hull Deformation

Ii the clraft at lnid iength is not equal io the mcan of the drafts at tl::F & A perpendicular it inclicatcs that the ship is hogging oI s.rgginiThc r-nean rtraft is thc mean oI the drafts at the F & A perper1diculars\\hen sagging, thc displacement obtainetl for thc mean clraft u'oul.l rlcss ancl uhen hogging, it rt 'oulti be morc than the actual clisplaceme:-of the ship in that condition. Thc hog/sag colrection to the clisplaceme:'is gencrallr. cffecled Lry obtaining the 'mean o{ ncans, rvhich is

F.dr.rft + A clraft + 6 r Amiclships

or as .l/.1 mean riraft +3/l Amidship's clraft.

First Trim Correction (Layer Correction)

This is thc nolmal correction to obtain the ttue mean draft of the !ese:the drait at the CF) ancl is obtanecl as

him x dist of CF fron mid point bet$'e iculars

LBP

u,hcrc irim is the ciiiference bctu'ccn thc cirafts at the Ij&A perpcndicula::This correction u'ill obvioush' be positive if the CF js closer io the c:.:to u'hjch shc is t l immed, than the miclship point. It not, the correctri r ' r ' d . r t i \u . lh i \ cor rec t ron app l ieJ lo t l re r r .an o f n re , rn . ' g ivc - : - .truc rncan draft. The displacement oi the vessel is obtainccl for thc t:::mean clraft oi the vesscl frorn hcr rlisplacernent scale.

Second Trim Correction (Nemoto's formula)

Thc fjrst trirn corrcclion is based on the assumption thai, \\41en a sl-::tr ins, shc trims iboui a fi\ed poini i.e. the CF ai thai l\ 'aterl ine. B::thc CF itsclf changcs u'hcn a slrip trinrs. Thc CF rotatcs in Lhe arc

o

draft

t 9 6

. . ' . l ' u r l r hn t l he ! \ . , i t e r l j nc i j alwavs tangential to the arc at the CF.

ry'qryfL]1\4Sfcr, MCrc,)LBP

l**l:. (nla.la,

f -

YCT:J is ttre cliffer.ence betu.een thc N,rCt.Cs for draftsl cms greater and 50 cms. Iesser than the mean oi -Itr"or_, 'iror,,

ntihc ressel. Thc correction in tonnes ma), also be obtained as

{s thc CF moves in the arc of a circle lt hcn the trim clif{ers from that::l-

tl'tl"n ,the

ships. clisplacement scale is proviclecl 1ofl,lori inruriuL,fl fn,:1'rc e'en kcel condition), a further ..rrr".ii,u., fr"l.i"". '""*r"".r,. .

fi".orrccrion in tonncs to thc clisplacemen, .r,u""J - lrl"ini.''lr' ,rii"r.r"u

".

::T.:^"qi:,, anct, TPC.) are the TpCs at drafts 50 cms. grearcr anct c0.nts tesser than thc mean of mean drafts_ This correctio"n in tonnes is.]ll'i:^

i.]:]_f "" to,the disptacement because, u.hen the CF moves rn the',1'"J:

il;i1 ",:,l-' "*l!:.""rf l.il" i,'" irnmersecl r' i"' o""'tin'''' i"'si gni rican t

rs plo'icle.l by more than ..'tt"a."tt for \'\'hich thc clisplacement scale

50 x (tfim in m),LBP

r 9 7

Correction for List

Thc ship should prcferably bc upright when conclucting a draft survellf the vessel has a iist she rises bodill' as thc imncrsed u'edge is largcrthan the emergecl wedge, particularly on ships with a large flare. Thisreduces the draft of the vessel. Thercforc thc following corrcction which.is ahvays positive is applied to the dispiacement.

Corn. in tonnes = 6 (d, - dr) (TPC, - TPCr) il.hen d, ancl d, are the clratt:an-ridships on the immcrsed and emerged sides respectivel]' and TPC' ancTPC" the TPCs for those respective diafts.

Density Coriection

The ship's dispiacement scale is provided for a stanclard density oI rra:.:usuallr, l.025 t/mr since other standards are also used, it is impor:.::to check the value used for thc displacement scale provided. The -,th_: idisplacement is then obtained as

scale dispJacement , den5it) of !\atcr

densih' used for displacement scale

Constant

If a draft sun,ev is conducted when the ship has no cargo on t'o::.gthc clifference between her actual displacement obtained from the displace..=.:cscale and displacement obtained as the sum of her light displacement :r.lall other, known weights on board then, would give the ships 'consl--:"i.e. the \a'eights of spare propeller, cylinder liners, stores etc. onLr .:(which do not form part of the ship's, light wcight). An abnormalh. s::or large constant points to an error in computation. The results sh--.jthen be re-checked. The 'constant' would alter over a pcriod oi -_as a result of additional equipment, accretion of stores, effect of corr(-sletc. This increasc in constant' with time would obviously vary from ::to ship. As a rule of thumb, it has been suggested that after,n ..:

1 9 8

: her life the constant' mav be cstimated as (0.5 +.hip's deadweight. The 0.5?i is for the rapid increase::'.e first vcar of her life. Other estimates suggested--rlps l ight displacement for every Year of service or 2.5r lears of service. Ho\,\'ever none of the above are\aat values.

0.05n) % of thert'hich occurs in

are 0.2596 of thex TPC for cvery

likelv to provide

Factors Influencing Accuracy

l..e clrafts must [)e observed accurately, prcferablv using a boat io obtain-!' Lrest acculacv possiblc. ldealll thcre sllould be no nar.cs or cutrent/

::. ie running r,hen the drafts arc observed. Anv .wave disturpancc orirr. \\'ater surface rvill influence the accuracy of the observcr.l clratts even: dralt gauges are used. A tide or current running u.ould procluce a'ri1cl up of rvatcl against thc loading edge and also.r1.1uat, rlhich r,r,ould::rect the clrafts observed.

-hc clcnsitv of water in irhich the ship floats uscd to calculate the ships

.rrsplacement must be bascd on a representativc sample of thc water, takcn::!rr1 at least three positions aiong the ships length, arva1, from discharges::,rn thc ship, at various depths, o11 thc side awav from the qual to:,-oicl anY clischarge from the shore and to aroirl an1, si2gn6n1 rvater trapped--.tween the ship and the jettv. A \-eighted container u,ith a perfotatecl:. i loi{ercd to the dcepest draft and raiscd .rt a constant speecl u,oulcl-irsure a fail lv representative sample. However, even this mav not ensure:;curac\' r l4rere stratif ication of r,vater laters erjsts. Wherr thc under kecl:.earance is small ancl the sea bcd is of so{t mud, the densitv o{ the,ner laver of watet can bc as high as 2.00 duc to the mud in suspensjon.: is impracticable to allow for this cffect u,hich tends to reduce the loaded

-rr-alt i.e. unclerestimate the loaclcd displacement.-hc

.lensity ancl temperature of thc water samples should be measured' lhe f i rne the . l ra f ts . t re nhrc r rc . l a . thc dens i t r \ r r ie5 u . i th the s ra te

't tic1e. To measure densitv, a glass h\.drometer designed for !^ ater, not' i l , should be uscd as the surface tension <l1 \\atcr.rn,l oil differs. Brassrstrulrents aLe not accuratc enough for this purpose. lVher-r reaciing the.\'rlrometel anv parallax error shoulcl be avoided and it should be ensurcd

::r.rt no air bubbles adherc to the submergcd position o{ the instrument.\s is ofien the case if the h\,drometer is calibrated for tvatcr in vacuuml)l-11 should bc subtractcd from thc hydrometer reading to allolv for the

' eight/., olur.r.re relationship in aii as compared to th;t in vacuum. If:1..e h'ater is not at the caiibration temperature of the instrument (usually'L) F), a further correction supplied u'ith the instrument must be a1,plicj.

. he exact weight of liquids in the tanks must be obtainecl bv obtaining:heir acculate ullages and making due allowance for the shipb trim and.-.nv list, using thc corection tables provicled with the tank calibr.ation tables.lhe correction tablcs shoulcl take into account the effect of the liquid surface

touching the top or bottom o{ the tank. The dcnsiiv of anYthc tanks should be mcasured as it mav differ considerablyof the rvater in u'hich the ship floats.

Whcn the anchors and cables are do\\'n, the disPiacement \\'ouldbc lcsser than whcn thev arc housed.

ballast ir.from that

obviou sl..

It should therefore bc obvious that accurate calculation of the quanii:of cargo onboard woultl depend lalgely on the skill and carc cxercisL-bv thc inclividual-rvhich is diflicult to quantify. If carrietl out carefullit should be possible to produce {airl,v accurate results

Evcrl el{orts should be madc to ensure that the bill of lading does r.i:orerstate thc quantitY cargo loaded. Shoulcl short delivery claims rrr-it is possible for thc ou'ners to contest such claims bv sho$'ing that ir=bill oi loacling quantitv is incorrect. h this, the shiP's dctcrmination --

the cluantitl at the load port and discharge Port is of considerable importar'..not necessarily in terms of absolute accuracy but in terms of consisterii.e. a common yarcl stick (the shiP itself) having bcen used for t'c:-mcasurements. If it is also shou,n that no cargo has becn lost duri::the voyagc (bv reference to log books) and that all cargo loaded has h-.-clelivered, it gocs a long wa,v in overturning the bill of lading figu-.

SHIP SQUAT

Squat is the decrease in under-keel water, that is, the difference beth,eenher under-keel clearancc when making rlal, and rvhen,i.oo".i o"", ,f_r"$'ater. It is not the increase in draft as

-visualiy ,"u.i or"u" shoh,n ondiaft inclicators.

Bernoulli's theorern states that in an). moving fluicl, the sum of the potential(nerg!. the kinetic energf an.l the pr.rsui. en.:rgy is o anrlr*ni. lh(:u : , , , .n " , .

the sh jp - i s f loa t ing in tha t wJ ter docs no t . r l te r the lev r - . l Inelgnr ot w.rter thcre. Therefore the potential energy of that warer tsunchanged. As the vessel makes way through the *ut3r, "fo

t"uuc" frellinaa hollon' in the water, The watei . theref"ore n.*" uit

-uf.,.,g the ship,ssicle ancl under her boftom ro fill in the hollow f"ii U"f1i-n? tl".ntp.As the water fiows aft, its kinetic energv increases. According to Bernoulli,s

;l::l-:,:I" ,t':,ll*1i. energy or the *nr", in.,"or"r. itt p"res,ur. en.rg'

l l : . : . : . "1" . - " : , s in(c rhc sh ip is . .upporrcd bv thc prcs iure energr n frne water, as Lhc pressure energy has reduced, the ship sinks to a longerdraft. In addition to the bodiiy sinlage that o..rlrq if,"-.iio''u,ro ,.,-,bv the head or by the stern. With I

"tuti. "u".,'t"l i oii l, 'f,.,ff for,r,vessels such as tankers and bulk carriers with Co more than 0.2 trir-ll bYthe head. Fine form vessels such as passenger ships and containe.s rlesseis

::t:.,-c:...1:": ,1.rii.,07. trim by_.the itern. " wr*i a -. .i"o.i'ir," ,q.",rs onlv uue, to bodil l sinkage. The overall clecrease in under_keel clearance(rue ro slnkage Jncl trim is lhe 5qudt forwarJ or aft

The factors that affect the amount of squat are

1) The ships speed over the water.

lh", 1C,1u, varies

. appro\ imately directly as the speed over the water

:: _K:o,rs .squdred. Squat occurs even when thc ship is moored,]i.,: :;t:. I i1"". ' lC

A,. srdreJ Lrnder. rhe chdprcr on iratt suncy,.rnrs snolrld be taken into account when conducting draft surveys.Also, when loading to a particular draf, squat .oulj r"J in unao,loading if the drafts arJ read when , t ia" i, .unninn.'

2) The block coefficient, Co

11: rq:".varie_s directly as the Co.. The Co lalues generalt), varylrom about 0.85 for very large tankers to about 0.ZE for buikers,

:::^11-0.1 _tg. generat cargo veisels to "U*t

O.O * r*r-# p,,"".g",vessels and container ships.

3) The blockage factor, S

The blockage factor, S, is the ratio between the immersed cross sectional

area ofcanal.

thc \,essel ancl $ atcr in thcthe cross sectional area of the

b x static draftS B r depth of water

Where

Lr' is the breadth o{ thc shiP ancl

B is thc width of thc canal.

Elcn in opcn $'aters, this factor is to bc considered using the wiclth

of inJluenie B' in Place of the wiclth of the canal B The u'idth

of influence B in oPen $'aters is obtained as

[7 .7 + 20 (1 - Cb)r] b

rvhere b is the breadth of of shiP.

The B value in oPen $'aters varies from about 8 b for large tankers

b about 9.5 b for general calgo vessels to about 12 b for container

and passenger shiPs.

ln open *'aters $'herc the dePth of water to draft of ship rattc'

is about 1.2, the value of the blockage factor S wil l be around 01

The static under keel clearance

Thc lesser the unrler-keel clcatance, the more is the squat becaust

the stream lines of return flo\\' aft of the water, past the vesse

increases cluc to thc reducccl clearance undel the vesscl This incrcascs

the kinetic energt ancl therefore {urther rcduces the Prcssulc cners

of thc watc!. iirus as the ratio of clepth of lvatcl to draft of sl-rr;

reduccs, the squat increases-

The at rest trim of the vessel

lhe squai at the bou' increases to a Sreater extant if hcr at re::

t l in was bv the head The squat at the stern $'i l l- incrcase tr

a grcater cxient if her at rest tri]n $'as bY the stern Thc calculat' -

-iri^lrlrl squat shoulci therefore be appliecl to the Srcater of tf'

ti{o crld drafts to obtain the minimum uncler kecl clearance

Passing a othei ship in a river or canal

When the ship is passing or overtaking another vcssel in a l ire:

or canal, the'".1.rof .on increase uPto t$ice the normal lalut ;"

ihe combincd blockage factor, S, becomes the sum of the block'ri'

factor of each ship.

B '

4)

s)

6)

222

n The squat increases if the ship is close to the bank of a riveror canal

Various empirical formulac ha!c been suggestecl for cstimating thcnaximum squat. As there are so manv variables and so inartrf . r r ro rs , the , \< r ! t ta lucs o l hhrch rn . t \ n , , i be r t ,a . i i l r a r , , i l . rbh , . r ro r r , .of the formulae are l ikelv b ptovicle absolutelv accuiatc squat valucs.Honcver, from thc analvsis of ntany measurcd squat valucs on shtpsantl results of ship model tests some empirical iormulac have beencleveloped for satisfactori l) ' estimating the maxinum squ.tt is coniinccland open h'aters. Obviousiy the squat is greatcr in ionfinecl $,atcrsand lesser in open n'aters.

For a vcssel at an cven kccl static trin when the ratio of the dcpthof $,atcr to the draft of ship is in the range of 1.1 to 1.1, ihenaximurt squat in open or confined lvaters may bc preclictcti fairlvJccur . r te l t b r ' " r (her , , f the er l re - r jo r r * -

r) Maximun squat

2) Maximum squat

C,. x S"' r v: 'x

20

a ! e 2 / r , \ / 2 $

30

i\.here s.' t -s

In thc above expressions:

S' is the blockage facbr.

V'is the ship's spcecl ovcr the u,ater in knots.'S. is thc velocity return factor.

'As is the immerscd cross scctional area of thc ship.'A,' is the cross sectional area of the rvatcr in the canal.

: t l

Ot l r , r appror imate fo r rnu lae are -

1) Maximum squat in open waters

2) Nlaximun squat in cor'\fined u'aters

rvhcre S is bet$,ecn 0.L anci 0.265)

1)

2)

3)

5)

o)

n8)

Atcan

C, . r V l

100

50

Both the atrove approximatc formulae slightlv over estilratcs imaximum squat thereby erring on the safer siclc.

lndications that thc ship is in shallon' waters include

Wa.,'c making bi' the ship, especiallv forward, incrcascs.

Manoeuvring LTecomes sluggish.

The propcllcr RPN,I rccluces.

Thc ships speed over the water reduces.

5 lnpp ing L l l s t . r l rccs anJ t rme increaser .

Thc cliameter of the turning circlc incrcascs to a great extcr:

Roll irrg and pitching reciuces.

The ship mav start to vibratc.

this point, a consideration mav arise as to the depth of u'atcr r'.be consiclered shallow. This clcpcnds on the clcpth of influer..-

t l.rc ship, nhich is approximatel\, { "

atuf,. In depths above thc .:-:

of influence thc ship may be considered to be in dccp rvaters. ln,].:belon' the clepth of ir.rfiuence, the ship may be considerecl in shallorv r.,":Sirrcc thc clepth of influence is morc than 5 times the rlraft, thour:ship's squat mav co[lmencc to increase slightlv at such dcp hs it .,oi rruch consequence. The incrcase in squat is significant rvhen tl 'ru:.to drafl ratio is less than 2. lt is much more pronouncecl anr.l of consec::.rr ' lrctt t lr i. ratio is less th.rn ]. i.

The best course of action to reduce squat is to rcduce the ships ,:Lrecausc ihe squat varies directl]' as thc ship s speetl squarecl. H.thc spccd $'i l l reduce the squat to a quarter. Ho."vever, the ta.:rnanocuvrilrg which is alreacly sluggish in shallow waters mar' ,.jc:.:furthcr shoultl also be considcrcci whcn rcclucing the speccl.

:2.1

.leel riue to interaction also occurs $'hen passing or overtaking another

,."."1 ;" "

narlou' channel ancl also when close to a bank ln shallou'

rr atcrs, heel due to turning [laY also increase, further reducing the uncier-

ieel clearance. This fact should be borne in mind rvhen turning h'idc

bocliecl vessels, with small GM at relatiYelY large speccls. The increase

rn ciraft due to heel, list or roiling can be surprisingll' large and in shallou'

uatcrs it coulcl cause grouncling at the bilge strake of the midcile boclv

ior instancc, thc increase in draft, given bY the exPresslon

(old draft cos ewith a draft of

+ 1/2 beam sin e) - oid c-lraft for a 50 m beam vcssel

12 m at a small heel of 30 is 13 m

229

When a body moves in a circular path, it experiences an accclcration to$'ar(ii

HEEL DUE TO TURNING

the circle -, where v is the velocity of the boclf in mI

the radius of the circie in meters. The force requirerl ir

mv'zacceleration is , where m is the mass of the bodv. Thts

I

the centripetal {orce acts at the centre o{ Iateral resistan(:i.e. at the centroid of the projected unclerwater lateral are.which is a point at about the level of the centre of buovanc.half the draft. This force is provided by the watcr actinFof the ship away from the centre of the turning circle.

the centre of

sec ancl r is

prociuce this

forcc calledof the shipof thc ship,or at alrouton the side

For equil ibrium, there must be an equal and opposite forcethc ship. This force called the centrifugal force acts at the centreof the ship, in a direction awav from the ccntrc of turn.

These two equal and opposite forces, i.e. centripetal force andforce produce a heeling couple

acting o.of gravit\

centrifugal

= v:: ^B,zr

Tire ship will then heel until the righting moment, W x GZ equals thehceling couple.

l5

l t 0

Therefore, when equilibrium attained

Since GZ

n.g .GMs in0

WxGZwhich ism.g .GZ= -! ' BtZ where B,Z = BG cos 0

CM sin 0

- . D ( l C O S H

I

r

- , DU COS tJ

. . g . GM s in 0

GM sin 0

i.e. tan 0

Since B is at

g. r .GM

about half tltc clraft,

tan 0 also- ; )

g. r .GM

In thc normal casc, rl,hcre G is above B, thcfrom the centrc of turn. In rate cases, wltcreship $'i l l hecl to$,ards the centre of turn.

_ v . [KG

ship $,jll l.leci a!a'alG is belou B, thc'

ROLLING PERIOD

The unresisted rolling period of a ship in still ra,ater

2nK'

ic GM

ihis expression should not be usccl to estimate her Glvl from hcr periocl,r ro11 at sea, as her actual rolling period is tl-rat of rcsisted rolling ancl

:r.rt unrcsisted roll ing. AIso, when roil ing at sea, the ta,atcr is not sti l l::rrl the rolling mav be Iorced oscillations due to a seawav and not entirely:,rc oscillations. Ir-urther, the radius of gvration K can at best bc onli,.:1 approxlmatlon.

Determination of GM' by Means of Rolling Period Tests(for ships upto 70 m in length)

ru approximation of thc initial GM in smail ships (upto Z0 m in length)

be ob t , r inc r l b ) th ( e \p re \ . ion CV fB

' * t r , , r "

:s thc lolling cocfficient (r-,'hich i'aries from about 0.88 lor the shipr.rallasl to about 0.73 for the fullv loacied vessel \,\,ith about 5% ofclcaclr'r'eight being liquicls in tanks,

= brcaclth of thc ship in m and

per ioJ o f r t ' l l i n sec , 'nJ -

. rolling coefficient varies $'ith the radius of gvration. A long rolling:.'cl corresponding to a GM of 0.2 m or lesser indicates lo\a. stabilit\,,

' :he accuracv of thc GM obtained is rcduced. The rolling period tcst:id be conducted in port, in still waier.

:.:mination of GM b1' rolling period tcst in open disturbecl n,atcrs, evenrelcd the oscillatior-Is are Iree and not forced os.iilations due to a.rv must be considered as a verv approximate cstimation onlv.

2 1 5

lire above expression for GMn ma1' be reducecl to

,F=

Fitt

(f.

where

BF

DAMAGED STABILITY OF PASSENGER SHIPS

The ship shall meet the damaged stabilitv criteria uncler the following

assumPtions:

a) The ship is in the $'olst anticiPaLed service condition as rcgarcls

stabil ity.

b) Tire permeability of the various

Cargo, coal and store sPaces :

A \commuJat ion \pJcc( :

Machinery spaccs

Liquid Tanks:

compartments ate as follo\\'s:

60?;

95",i

85%

07" or 95% $'hichevcr resultsin least stabilit\'.

c) r) The longitudinal extcnt of damage is 3ln + 39i ot th!

ships leirgth or 11 m, ilhichever is lesscr' \'Vhere th'

facior of subdivision is U 33 or less, the longintudlna-

extent shall be increascd as necessal)' to inclu(le t\\'r

transverse bulkheads

ii) The tiansverse cxtent of dama€ie is onc fifth ihe ship:

breadth

iii) The lertical extent of damage is {rom the base' up$'rr':

without limit

\\rherc the ship's {actor of sLrbdivision is more than 0'5' she should t'-

able to withstancl the flooding of anY one comPartment Where trvo aeljacc: -

compartments are scparatcd b1' a stepped bulkhead, she shoulcl bc aL'-:

to withstar1d the flo;ding oi the two adjacent comPartments'

Whcre the ships factot of subdivision is 05 or less but more than 03:

she should be able to $'ithstand the flooding of anv two adjacent co::'

Partmen$.

Where the ship's factor oI subdivision is 033 or less, she shoulcl lT

to \\'ithstand the flooding of anv three adjacent conPartments

DAMAGED STABILITY CRITERIA TO BE SATISFIED BY PASSEN-CER SHIPS IN THE FINAL CONDITION AFTER DAMAGE AND

AFTER EQUALISATION MEASURES

In the case of synmetrical f looding, shc shall havc a rcsiciu.rl G\lof at least 50 mm.

In the case o{ unsymmetrical floocling thc anglc of heel sh.ill notexccecl 70 for one compartment fkroding an.1 i2, for tlvo or morecompartment flooding.

Thc margin l ine shall not bc submergeci at any poirlt.

11:: 9i,:::1"- tq have a posiiil,e rangc of at least 150 bq.ond ANGI_LOIJ EQUILIBRIUM.

Area under the GZ curve to be atleast 0.015 mrad between Angicof Equilibrium and lcsser of

r Either angle of progressivc flooding

o1

220 in casc of flooding of onc comparhncnt; 27,, in case offlooding of more than one acijacenf compartments

residuai righting lever is to be obtained of at lcast 0.1 n u,ithinrange specilicd in 4. above, taking into account the grcatest offollou'ing hceiing moments.

Heeling moment due to crowdi|tg of passengers onto onc sidcot

Heeling moment clue to launching of fully loadecl davit launchedsurvival crafts on one side

ot

Due to wind pressure.

thethe

I

As calculated by the

CZ

formula

Heeling MomentDisplacement

211

+ 0.0f

ASSUMPTIONS FOR CALCULATION OF HEELING MOMENT

For calculaiing the hecling moments, the following assumptiorsmade-

1. Heeling r-noment duc to crowding of passengers to

r .1 perso l l s per squarc met re .

r rnass of each passengcr : 75 kg

! passengers at their muster stations on that sidcb rvhich she is listed

shall :t

one : : : :

oI the

or

2. Fleeling momcnt cluc to launcl-ing of fullv loadecl davit lau:::dsur|ival crafts o11 one sicle.

r Marimum heeling moment due to all l i feboats ancl rcscue :-;! ion the side to h,hich thc vessel has hcelecl bccause of rla::-:=ale srvullg oui fully loadcd ancl rcady for lowerlng.

r A frrllv loadecl rlavit launchecl life raft is slrung out ol ::i!clavit on the sicie to \.\'hich shc is listcd.

r For liieboats u'hich are launchecl iullv loadecl from the st.-'. eiposition, the maxin-run heeling troment is to bc take::

r Persons noi rn lifc saving appiiances $'lich are swun! 'tshall not providc heeling or righting moments.

r Life saving nppliances on the oiher siclc arc to bc ass:::-.::!to be in the storved posiiion.

or

3. Hccling nroment clue to wind pressure

r lhc nind prcssurc sha1l be assurner:l to be 120 N,/m:

I lhe \\ ' ! ldage areir is her projectcd latcral alca abolc the:.::=line, in the iniact condition.

r The heeling a1m is the \ 'erticai distancc L)ct\\,ccn thc ce.:: ,1of the $'irrdagc arca ancl half oI the mean dr;rfi i il-re ::--.:cond i t ion .

At .ritermediate stages of flooding the maximum righting lelcr sh.r1] be

ai lcast 0.05 m and the range of stabil itv shall be at lcast , .

-nsvmnetrical flooding is to be kept to a minimum. Wllere it is r1elcssarvio_ correct large angles of ircel duc to unsvmmetrical floocling, the mc,rns.rclopted shall be sclf acting where practicable. But where conhols arr]plolided to cross flooding fittings, thel must be operable from aLrove thcrulkheacl cleck. lVhere cross flooding fittings are provclecl, the tirue ior.qualisation should not cxceed 15 r]rinutes. The maximun anglc oi hcclafter floocling, but before equalisation shall not exceed 150.

Ihe master shall be supplied with neccssarv data to maintain sufficient:ntact stability to enable the ship to withstand the assumed damaqe. This.hall inciudc the maximum permissible KG or mininum pcrmisslble GM:or a range of service .lrafts/ displaceinents.

243

TANKER CARGO CALCULATION

Measurement of cargo

()n boarcl a tankcl the Inetl'rocl of caiculating the quantitl of oil on boarcis cli{ferent flom those as usecl in case of other ships. Here thc r,olumeof oil in cargo oil tanks (C.O.1.) is tabulated against clif{crent ullages ic:varr.ing conclit iotrs of trim ancl l ist. lt is rcquired of the ship's personne-io takc the uliages, n'ateldio of thc tanks ancl notc clown the irinr .lr-.ilist of the vessel. Norn-r'eferring to the ullagrs tables of the vessel concerne;volnr-r-re o{ oil in clifferent tanks is obtained.

On board a tanker thcrc are cliffcrcnt methods oi mcasur.ing ullage:Some of them aIe r| ith an u1lage tapc, Ullage Terrperaturc Ltteriac.(UTI)7 M\4C/Sonic tirpe, r\f iessoc gauge, raclar gauge etc. Silnihrlv soundin.:can also be obtainccl using a sounding rod, sounding tape etc. l\ iatrrclt l.watercut is also measuted n'ith a UTI/NIMC.

Corrections to the Observed U'llage

The ullagc thai is obiainccl bv using ar-rv o{ the abo\,e nethods is:L-re corrccted ior the prcscnt t l im ancl l ist of the lessel. Also thc iocari.:of uliage port is takcn inio account, i.e, its height, l-rou- far i l is iorh;,:.:ot thc aftcl bulkheacl oi the tank an.1 bl rvhat distance it is Jisflac.:i ro rn t l r - c . t r le r l i r r - , , - r l . c r r rL l

The Liquid Strtface Insirle TIrc Tauk Rcnutitls Horizolttal lrfesl,c(tfue ()-TItc Trifit Altd List Of The Ycsscl.

Consider a vt-ssel or. even kccl an(l upiight. Since the litFrirl sur-face $,i l l be horizontal, t lrc sarne u11age $.i11 be obtainecl i lrespccti. ioI u'here thc ullage port is located.

Norv consider the same vcssel trimmed by stern

'1:' Length of the tank ABCD

'UO' Obsen,ed ullage

'UP' Ullage conectcd for rape correchotl'LrT'

Ullaged correctecl for tape ancl trim correction'e' Tdm angle

: the ullage is measured *,ith thc, help ot an ull.lge tape or MMC/ UTI/-,nrc tape/ clue to the trin of the vcssel it wil i ,ou'.fr if,. lactuat oit-::r'tace' at right angles and hence the observecl ,fUg" *."if

"le ,UO,.-.us ihe observecl uilage is to be correcte(l for.both tape Xnd trim cor.cctions.

: a, n'hessoe _gauge or raclar gauge had been used the Iloat in case of'.,hcssoe and the radar bean.r in cise of raclar gauge ,"*fJ'fluru tru""I"a::.rl lel to the bulkhead of the Ir, ''us the observcd ullage o'i:"oJx1,il",":o;:i';j,,."i:n.l.T,:"i:

1 . . n 1 . , , n . , t j o n i j n e c c 5 . d r |

In both the cases the corrected ullagc is 'UT' as shown above.

Tape Corection

UOUP

UP

tan 6

cos 0

UO x sec 0

trimLBP

Thus UP = UO

He ce Ull@ge coftected

= obserued

f . /trim)lx sec ltan'' I Ji

for tope coftectiotr

[ . - . (mn\]ul lage . sec \ tan \ ror l l

Hence UT =

tu im ( ! )LBP \2 )

UP+x

up * ( |

o \ ,H*\2 ) LBP

At the same time if the vessel was also listed to portport was located 'b' m to starboard of the centreline o{the ullage corected for the tape and trim corections isfor list also.

tan 0

Thus UT

and the ulla::the tank, tLe:

to be collecte:

246

As shon'nto port.

in the fig. Below consider the same vessel to be listed <|

tan O

XT 'x tan< i

bx tan( r

T'PXT'

T 'P

LlSr Lotr.

i .ncc ln this case, the ul lagc ooe arrJ rirc ,_,,", ,.',,,i"1".,.u01i,.''J.:T:ir.J;":[".i:,i:";.ji,lo,#,Jlr.rJ thc list and thc location of rtilage port

_ bcen to thc samc slde ofi:iler tlne, the list correclion has to be *i.l"d t,l .froi" ,ifr"'or"

,1"g".

Thus finally the corrected ullage, taking into aqcount, both list and trjm

conection is to obtained as follolvsl -

1.

2.

Corlect the observed ullage for taPe correction

'fo this corlectecl ullagc appll tr im and lisi conection

Trin correction to be addecl it thc vessel is trimmccl bV stern.

T-ist corection to bc aclded if l ist and location of ullage port

is to sane sidc of centerline otherwise if of tlifferent name,then to be subtracted.

I

I

CotectedUllage

Lengih of the tank

Location of ullage Port

Location of ullage Port

Anglc of list

l 't trit' tletl ollage . rc.

lrat' I 16p )i

l l ,n\,!vt] ta.,n,,,L\2 t LBP)

forlvard of a bulkhead

awav from centie line

= obsefi)

Wherc

t:

,b,

(I