ship stability formule

8/13/2019 Ship Stability Formule

1/12

Summary ofstability formulae*

Form coefficients

DraftsWhen displacement is constant (for box shapes):

When draft is constant:

Homogeneous log:

Draft

Depth

Relative density of log

Relative

ddensity of water

New displacement

Old displacement

New densit

yy

Old density

TPC WPA

97.56

FWA W

4 TPC

Chan

SW

SW

gge of draft or dock water allowanceFWA 1

( 0025

25

DW )

New draft

Old draft

Old density

New density

Area of waterplane

L B C

Area of amidshipsw

BB d C

Volume of displacement L B d C

C C

m

b

b m

Cp

Appendix I

* See Note at end of the Appendix


2/12

Variable immersion hydrometer:

Trim

Effect of trim on tank soundings:

True mean draft:

To keep the draft aft constant:

To find GML:

Simpsons rules1st rule:

Area h/3 (a 4b 2c 4d e) or CI13

1

GM

GG

L

tL

1

d MCTC L

TPC l

Correction

FY

Trim

Length

Head when full

Length of tank

Trim

Length of

sship

MCTC W GM

100 L

Change of trim Trimming mome

L

nnt

MCTCor

W LCB LCG

MCTC

Change

foap foap ( )

oof draft aft l

LChange of trim

Change of dr

aaft forward Change of trim Change of draft aft

DensityM

M x M ML

y

yy x

486 Ship Stability for Masters and Mates


3/12

2nd rule:

3rd rule:

KB and BM

Transverse stabilityFor rectangular waterplanes:

For box shapes:

For triangular prisms:

Longitudinal stability

For rectangular waterplanes:

For box shapes:

BM L12dL

2

I BL

BM I

V

L

3

LL

12

BM B /6d

KB 2d/3

Depth of centre of buoyancy

2

1

3

d

2

V

Abelow the waterline

BM B /12d

KB d/2

KM B/ 6

2

min

I LB

12BM I/V

3

Area h/12 (5a 8b c) or CI112

3

Area 3h/8 (a 3b 3c 2d 3e 3f g) or CI38

2

Summary of stability formulae 487


4/12


For triangular prisms:

Transverse statical stability

Moment of statical stability W GZAt small angles of heel:

By wall-sided formula:

By Attwoods formula:

Stability curves:

W ship displacement in tonnes

GG horiz movH

eement of G

GG vert movement of G

rV

o

l iighting arm @ 0 if upright ship

ri40

( )

l gghting arm @ 40

HM heeling moment

SF sto

wwage factorVHM volumetric heeling moment

l l lo 40 oTotal VHMSF W 0.8 Actual HM Total V

HHMSF

Approx angle of heel Actual HM

Maximum

ppermissible HM12

Approx angle of due to

grain shift

Reduction in GZ GG GH ( cos ) ( GGV sin )

New GZ Old GZ GG heel or

New GZ KN KG sin h

1

sin

eeel

Dynamical stability W Area under stabil iity curve

W v(gh g h

VBG(1 )1 1

)cos

GZ v hh

VBG1

sin

GZ GM BM122 ( tan ) sin

GZ GM sin

BM L

6dL

2


5/12


List

Increase in draft due to list:

Inclining experiment:

Effect of free surface

Drydocking and grounding

Upthrust at stern:

or

Pressure of liquids

Pressure (P) Dwg

Thrust P Area

Depth of centr

ee of pressure IAZWL

Virtual loss of GM P KM

W

or P KG

W P

P Old New displacement

P MCTC tl

Virtual loss of GM lb

W

1

n

3

2

12

GM

GG

Length of plumbline

Deflection1

New draft b (d) . . . Rise of 1

2 sin cos ffloor is zero put r in if rise of floor exists. (measured at full Br. Mld)

Final KG Final moment

Final displacement

GG1

ww d

Final W

tan list GG

GM1


6/12

Bilging and permeability

Strength of ships

Youngs modulus:

Bending moment:

Shearing stress:

Stress:

Freeboard marks

Ship squat

Blockage factor b T

B H

C S Vmax

b 0.81 k2.08

220

Distance Summer LL to Winter LL Summer148 ddraft

Distance Summer LL to Tropical LL 1448

Summer draft

f E

Ry

q F y

I t

M ER

I

Section modulus I

Y

E Stress

Strain

Stress Load

Area

Strain

Change in length

Origi

nnal length

y

R

Permeability S

SF100 per cent

Increase in d

rraft vA a



7/12

In open water:

In confined channel:

Miscellaneous

Angle of loll:

Heel due to turning:

Rolling period:

Zero GM:

Theorem of parallel axes:

I I AyCG OZ2

tan list 2 w d

W BM3

T 2 k

g GM

2k

GMapprox

tan heel v BG

g r GM

2

tan loll 2 GM

BM

GM 2 initial GM

cos loll

T

maxb k

2C V

50

Width of influence 7.7 20 C(1 bb)2

maxb k

2C V

100

y H T

y y

A b T

A B H

o

2 o max

s

c



8/12

or

Permeability ()

Drafts and trim considerations

Alternative form correction

50 True trim

( )22 2 ( )MCTC MCTC

LBP

1

Second trim correction for position of LCF, if trimmedhydrostatics are not supplied a(form correction)

True trim MCTC MCTC2 1

( ))

2 TPC LBP

Correction of midships draftto true mean ddraft whenLCF is not at amidships

Distance

of LCF from midships Trim

LBP

Midships draft corrected for deflection dFP

( )6

8

d dm AP

Correction to observed drafts l

L

Trim1

1

Permeability BS

SF100 per cent Increase in d rraft

A a

Permeability ( ) Volume availa

bble for water

Volume available for cargo10 00

Permeability ( ) SF of cargo solid factor

SSF of cargo100

Solid factor 1

RDEffective l

eength l

Sinkage Volume of bilged compartm

eent

Intact waterplane area

Tan BB

GMH

bilge

dd

I I AyNA xx2



9/12

NoteThese formulae and symbols are for guidance only and other formulaewhich give equally valid results are acceptable.

(L B d) Cb

DWT light

AW (L B) CW

MSS GZ

GZ GM sin GZ [GM 12 BMtan

2 ]sin

GZ KN (KG sin )

Dynamic stability Area under GZ curve

Actual HM Total VHM

SF

l

l l

o

40 o

Total VHM

SF

0.8

Area under curve SR1 1

3h y 4y y

Area

1 2 3( ) ( )

under curve SR2 38

h y 3y 3y y1 2 3 4( ) ( )

FWA4 TPC

DWA FWA

Summer

SW

dock

( )1025

25

Sinkage/rise W

TPC

TPC AW

100

RD substance

FW

Mass

Volume



10/12

Reduction in GZ

(GGH

cos ) (GGv sin )

tan 2 w s

BMT3

GM at angle of loll 2 initial GM

cos

tan angle of loll 2 GM

BMT

GM w s length

deflection

GG Moments

WeightsH

KG

Moments

Weights

tan GG

GMH

FSC FSM

FSC l b

12

3

T

FSC i

T

GG w sH/V

Rolling period T sec 2 K

g GMor

K

gGM

2

T

( )

2

or K

GMseconds

2

T

2

Approx angle of heel Actual HM

Max permissib

lle HM12



11/12

Loss of GM P KM or P KGP

T

P Trim MCTC

LCF

P Reduction in TMD TPC

Trim LCG LCB

MCTC

( )

Change of trim aft Change of trim LCF

LBP

Cha

nnge of trim fwd Change of trim LBP LCF

LBP

T

uurn mean draft Draft aft trim LCF

LBP

CoT Trimming moment

MCTC

MCTC GM

100 LBPL

KM KB BM

BM I

BM box L B

L L

LL

L

3

( )

12

Distance Summer LL to Winter LL Summer 1

48ddraft

Distance Summer LL to Tropical LL 1488

Summer draft

Draft when heeled Upright draft ( cos ) ( 12

bbeam

Position of the metacentre

sin )

( )

KM KB BM

BM l

BM box L B

T T

TT

T

3

12



12/12

SummaryAlways write your formula first in letters. If you then make a mathematicalerror you will at least obtain some marks for a correct formula.

Alternative form correction 50 true trim

2 (MMCTC MCTC

LBP12 )

Second trim correction for position of CF iff trimmedhydrostatics are not supplied f( oorm correction

True trim MCTC MCTC2

2 1

)

( ) TTPC LBP

Correction of midships draft to truemean drraft when CF not midships

Distance of CF f

rrom midships trim true trim at perps

LBP

( )

Midships draft corrected for deflection dFP

( )6

8

d dM AP

Correction to observed drafts l

LTrim1

1

Tan BBGM

H

bilged

I I Asparallel axis centroidal axis2

Sinkage Volume of bilged compartment permea

bbility )

Intact water plane area

(

Effective length l

Permeability SF of cargo solid factor

SF( )

of cargo100

Solid factor 1

RD

Permeability Volume available for water( ) VVolume available for cargo

100

tan

v BG

g R GM

2


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