Ship tecnic Sharif university Lecture 5

8/4/2019 Ship tecnic Sharif university Lecture 5

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Chapter 5

Ship Stability


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Contents

1- Definitions

2- Numerical Integration3- Stability

5- Rules and Regulations


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Definitions :

Principal Dimensions (length, breadth, depth etc)

-Length.Lbp ( or Lpp) Length between two perpendiculars

FPForward perpendicular (vertical line through intersection

of stem and waterline (w.l).)

APBackward perpendicular (vertical line through the center

of rudder pintle)

LoaOverall Length

LwlWaterline Length (calculation length)

also see Table 6-2 at p142


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W.L.

A.P

Loa

Lwl

Amid Ship

Lbp

F.P.Forward Sheer

After Sheer

Sheer is the height measured between deck at side and base line.


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Line Drawing:

Using the methods of descriptive geometry, the form of

a hull is drawn on a scale (1:50 or 1:200) drawing,

which is called Lines Drawing, or simply the linesor lines plan.

Lines drawing mainly consists ofthree plan views

Sheer plane (Buttock plane, Buttock lines) : parallel

to the longitudinal central plane (2m, 4m, etc are the

distances from the center plane)


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Half-Breadth plane (Water plane, Waterline planes):

parallel to the base plane (2m, 4m, .are the distance

form the base plane)

Body Plan (Ordinate station, Transverse section,)

parallel to the mid-section (# of stations indicated the

distance from the mid-section or bow).

Diagonals (Bilge Diagonal)

Fair form and fairness of line, checking theconsistency of point, smoothness of lines

Table of Offsets


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Line Drawing


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WATERLINE

DEPT

H

OFHULL

DRAFT

FRE

EBOARD

RESERVE BUOYANCY


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Hull characteristics (coeff.)

Displacement and Weight Relationship

B (buoyancy) = W(weight). (conventional ship)

displacement B= =

Appendage volume 1%


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Hull characteristics (coefficients

(non-dimensional)

- Coefficient of Form ( Fatness of a hull)

Block Coefficient CB

whereL= Lpp or Lbp and T= Draft

CB 0.38~0.90 even bigger

- Miship Section Coefficient

CM = immersed area of mishap section (A) / (BT)

0.67~0.98

BC

LBT


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-Prismatic or Longitudinal Coefficient: 0.55~0.80

-Waterplane Coefficient

-Displacement /Length Ratio

BP

M M

CC

L A L B T C C

area of water plane0.67 - 0.87

where --Length of Load water plane

= Beam of W.P.

WPC

LB

L

B

3 3

B

B

C LBT B TC

L L L L


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-Breadth /Length Ratio :

-Draft/Length Ratio

-Draft/Breadth Ratio

-These coefficients are related to the resistance and

stabilityof the ship and can be used to estimate

them empirically.

B

L

T

L

T

B


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Important Hydro-Static Curves or Relations

Displacement Curves (displacement [molded, total]vs. draft, weight [SW, FW] vs. draft (T))

Coefficients Curves (CB

, CM

, CP

, CWL

, vs. T)

VCB (KB,ZB): Vertical distance of Center of

Buoyancy (C.B) to the baseline vs. T

LCB (LCF,XB): Longitudinal Distance of C.B or

floatation center (C.F) to the midship vs. T


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Numerical Integration for

Ship Forms


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Representing the Hull Form


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The Body Plan


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Data of Ship forms

Discrete data (Line drawings, stations, water plane

etc)

Evenly distributed (most times)


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Methods of Numerical Integration

Trapezoidal rule (linear)

Simpsons first rule (quadratic)

Simpsons second rule (cubic)


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fn (x) can be linear

fn (x) can be quadratic


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Trapezoidal Rule

Linear approximation

)()()()()()(

10

1100i

1

0i

i

b

a

xfxf2

h

xfcxfcxfcdxxf

x0 x1x

f(x)

L(x)


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Multiple Applications of Trapezoidal Rule

)()()()()(

)()()()()()(

)()()()(

n1ni10

n1n2110

x

x

x

x

x

x

b

a

xfxf2x2fxf2xf2

h

xfxf2

hxfxf

2

hxfxf

2

hdxxfdxxfdxxfdxxf

n

1n

2

1

1

0

x0 x1x

f(x)

x2h h x3h h x4

n

abh


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Simpsons First Rule

Approximate the function by a

parabola

)()()()()()()()(

210

221100i

2

0i

i

b

a

xfxf4xf3

h

xfcxfcxfcxfcdxxf

x0 x1x

f(x)

x2h h

L(x)


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Multiple Applications of Simpsons First Rule

Applicable only if the number of segments is even


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Multiple Applications of Simpsons First Rule

n

abh

1n

531i

2n

642j

nji0 xfxf2xf4xfn3

abI

,, ,,

)()()()()(

6

xfxf4xfh2

6

xfxf4xfh26

xfxf4xfh2I

n1n2n

432210

)()()(

)()()()()()(

n must be even


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Simpsons Second Rule (single application)

Approximate by a cubic polynomial

)()()()()()()()()()(

3210

33221100i

3

0i

i

b

a

xfxf3xf3xf8

h3

xfcxfcxfcxfcxfcdxxf

x0 x1x

f(x)

x2h h

L(x)

x3h


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StabilityA floating body reaches to an equilibrium state, if

1) its weight = the buoyancy2) the line of action of these two forces become collinear.

The equilibrium: stable, or unstable or neutrally stable.

Stable equilibrium: if it is slightly displaced from its

equilibrium position and will return to that position.

Unstable equilibrium: if it is slightly displaced form its

equilibrium position and tends to move farther away from

this position.

Neutral equilibrium: if it is displaced slightly from this

position and will remain in the new position.


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Motion of a Ship:

6 degrees of freedom

- Surge

- Sway

- Heave

- Roll

- Pitch

- Yaw

Axis

Translation Rotation

x Longitudinal Surge Neutral S. Roll S. NS. US

y Transverse Sway Neutral S. Pitch S.

z Vertical Heave S. (for sub, N.S.) Yaw NS


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Righting & Heeling Moments

A ship or a submarine is designed to float in the

upright position.

Righting Moment: exists at any angle ofinclination where the forces of weight and buoyancy

act to move the ship toward the upright position.

Heeling Moment: exists at any angle of inclination

where the forces of weight and buoyancy act to

move the ship away from the upright position.


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SHIPS STABILITY

METACENTER

m

B0

F di l hi


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G---Center of Gravity, B---Center of Buoyancy

M--- Transverse Metacenter,

If M is above G, we will have a righting moment, and

if M is below G, then we have a heeling moment.

W.L

For a displacement ship,


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For submarines (immersed in water)

G

B

G

If B is above G, we have righting momentIf B is below G, we have heeling moment


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Upsetting Forces (overturning moments)

Beam wind, wave & current pressure

Lifting a weight (when the ship is loading or unloading in the

harbor.)

Offside weight (C.G is no longer at the center line)

The loss of part of buoyancy due to damage (partially flooded,

C.B. is no longer at the center line)

Turning

Grounding


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Static Stability & Dynamical Stability

Static Stability: Studying the magnitude of the

righting moment given the inclination (angle) of the

ship*.

(That is, the rolling velocity and energy are notconsidered.)

Dynamic Stability**: Calculating the amount of work

done by the righting moment given the inclination ofthe ship.


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Static Stability1. The initial stability (aka stability at small

inclination) &,2. the stability at large inclinations.

The initial stability: studies the right moments or right

arm at small inclination angles.

The stability at large inclination (angle): computes theright moments (or right arms) as function of the inclination

angle, up to a limit angle at which the ship may lose its

stability (capsizes). (Cross curves of stability (see Fig.

6-7 at pp 156) & Curves of Static Stability (see Fig. 6-8

at pp157) )

The initial stability is a special case of the latter.

S O S


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MAIN STABILITY POINTS

m metacenter G center of gravity

B center of buoyancy

m

G

h

a

B1

Q

Wo LO

W1

L1

Q

B


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Initial stability Righting Arm: A symmetric ship is inclined at a small angle

d. C.B has moved off the ships centerline as the result of the

inclination. The distance between the action of buoyancy andweight, GZ, is called righting arm.

Transverse Metacenter: A vertical line through the C.B

intersects the original vertical centerline at point,M.

sin

if 1

Small angle inclination

5 0.087266

GZ GM d

GMd d

d


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Location of the Transverse Metacenter

Transverse metacentric height : the distance betweenthe C.G. andM(GM). It is important as an index

of transverse stability at small angles of

inclination. GZis positive, if the moment is

righting moment. Mshould be above C.G, ifGZ

>0.

If we know the location ofM, we may find GM, and

thus the righting arm GZor righting moment can

be determined given a small angle d.


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; the distance from C.B. to

( ) the distance from the baseline to .

,

where is the vertical coordinates of the C.B.

The vertical distance between the metacenter

x

M

x

M B

B

IBM BM M

H KM M

IKM = H = + Z

Z

.

& C.G,

x

M G B G

IGM H Z + Z Z

E l f


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Examples of

computing KM

d

B

3

2

2

3

2

2

) Rectangular cross section

1, ,

2 12

12

12 2

) Triangular cross section

2 1 1, ,

3 12 2

6

2

6 3

B x

x

B

B x

x

B

a

dZ I LB LBd

I BBM

d

B dKM BM Z

d

b

dZ I LB LBd

I BBM

d

B dKM BM Z

d

d

B


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W L

DYNAMIC STABILITY


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ROLLING PERIOD

SHIPS STABILITY AND ROLLING PERIOD

W L

T= C B

GM

ROLLING PERIOD


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ROLLING PERIODThe rolling period of the ships dependenced from ships stability. The formula

Between ship,s stability and rolling :

T = c*B/sqr GM

In this formula:

Trolling period in sec.

c - constanta

Bthe ships beam to outside of hull.

Note: the constanta c dependenced from ships displacements.

There are the followings meanings:

c=0.88when ship is empty or ballast;

c=0.78 - when the ship has on board amout 20 %

c=0.75when liquids on board 10%

c=0.73when all liquids on board amout 5%

HOWEVER, for all lagers ships Lloyds Register of shipping and the 1991 HMSO

Code of Practice for Ro-Ro ships use c= 0.7


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SHIPS STABILITY VARIATIONS

FREE LIQUID AREA

P0

W0L0

C0

G0

M Moment liquid


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FREE LIQUID AREA

P1

W0 L0

C0

G0

m

M Moment liquid

M Moment upserting

P1

C1W1

L1

Q

Mcargo


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HANGING CARGOQ

lz

P

Mcargo= Pcargo lz sin Q

g

W0

L0

W1

L1


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Rules and Regulations

The rules and regulations are issued by organizations

which may be divided into three categories:

-Classification societies: have established standardsof construction by the production of rules which

have done much to ensure the safety of ships.

-Governmental Authorities: concern for the safety

of ships and the well being of all who sail the ships.

(behavior of the people)


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WNA

W

S

T

F

TF

PLIMSOL MARKS (Load lines)

Markings of minimum allowable freeboard for registred cargo-

Carryng ships.Located amidships on both the port and starboard

sides the ship.

Since the required minimum freeboard varies with water density

and severity of weather, different markings are used for:

- TFTropical Fresh Water

- F - Fresh Water

- T - Tropical Water (sea water)- S - Standard Summer

- W - Winter

- WNA-Winter North Atlantic

Classification Societies


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Abbreviation Full Name Headquarters

ABS American Bureau of Shipping N.Y.

BV Bureau Veritas Paris

GL Germanisher Lloyd Hamburg

HR

Hellenic Register of Shipping Greece

LR Lloyds Register of Shipping London

NK(K) Nippon Kaiji Kyokai Tokyo

NV(DNV) Norske Veritas Oslo

PC Registry of Shipping of USSR Moscow

RI (NA)Registro Italiano (Navale) Genoa


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Ship tecnic Sharif university Lecture 5