Stability Lecture 1

7/27/2019 Stability Lecture 1

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Stability : first principles

Ship theory


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A ship, like any other three-dimensional body, has six degrees of

freedom.

That is to say, any movement can be resolved into movements

related to three orthogonal axes, three translations and three

rotations.

Definition
http://en.wikipedia.org/wiki/File:Rotations.pnghttp://en.wikipedia.org/wiki/File:Rotations.pnghttp://en.wikipedia.org/wiki/File:Translations.PNGhttp://en.wikipedia.org/wiki/File:Translations.PNG


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Definition
http://en.wikipedia.org/wiki/File:Rotations.pnghttp://en.wikipedia.org/wiki/File:Translations.PNG


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Degrees of freedom

A ship, like any other three-dimensional body, has six degrees

of freedom.

3 translations :

Surge (longitudinal)

Sway (transverse)

Heave (vertical)

3 rotations:

Roll (longitudinal)

Pitch (transverse)

Yaw (vertical)


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Definition

Centre of buoyancy : geometrical centre of the underwater

volume and point through which the total force may be

considered to act vertically

Centre of flotation : geometrical centre of the water plane area


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Definition

Centre of gravity : point in a body through which the total weightof the body may be considered.

Remark: resultant moment about the centre of gravity is zero

How to calculate it?

System in equilibrium : F=0 et M=0

Force : F=0,

So :

Moment : M=0

Attention to the origin. It can be choosed randomly, but take itsmarlty.

51

... FFFR

R

ii

RRRRx

F

XF

XXFXFMMXFM551151

......


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Definition

If a weight is moved, added or

removed, the centre of

gravity will move

Effect of weight

displacement:M=0

So :

Effect of added/removedweight

RF

dFGG

1

FF

dFGG

R

1


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Definition

Plimsoll marks or freeboard mark :indicating the maximal immersion of the

ship in the water, leaving a minimal

freeboard for safety. The immersion will

change in function of the water density

(sea or fresh, temperature).

GL : for Germanisher Lloyds, for example

T : TropicalS : Summer

W: Winter

WNA : Winter North Atlantic

TF : Tropical Fresh


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Definition

Plimsoll mark and draft mark :

rules to respect (size, spacing,

etc)

Draft marks : on each side, infront, aft and middle of the

ship. Very useful to estimate

the displacement with the

hydrostatics.

Deck line: the extended line from the

upper side of the freeboard deck at

the ships side. Placed above the

plimsoll mark, so easy to measure

freeboard


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Definition

List : helling to one side

about the fore and aft

axis

Trim : difference between

the draft at the stern and

the draft at the stem


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Definition

Metacentre M : when the ship is heeling, the

centre of buoyancy moves because the

immersed shape changes. The metacentre is

the point around which the centre of buoyancy

rotates. The metacentre = intersection of thesuccessive line of buoyancy.

Under 5 , it is assumed that M :intersection of the

buoyancy and the centerline.

Beyond 5 , it is no more the case. So, M willmove.


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Definition

The metacentre can be longitudinal or transversal.

Notation :

Some remarks : centre of buoyancy moves with the ship

movement. Centre of gravity doesnt change (except loading,fuel consumption etc).

G: centre of gravity

VCG Vertical centre of gravityLCG Longitudinal centre of gravity

TCG Transversal centre of gravity

B : centre of buoyancy

VCB Vertical centre of buoyancyLCB Longitudinal centre of buoyancy

TCB Transversal centre of buoyancy


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Characteristic of water

The specific weight of the water depends on

the amount of salt and the temperature

990

995

1000

1005

1010

1015

1020

1025

1030

0 5 10 15 20 25 30

Density(kg/m)

Temperature (C)

Fresh water

Sea water


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Characteristics of water

Variation of the salinity


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Viscosity

Change of viscosity with the temperature

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 10 20 30 40 50 60 70

Kinem

aticviscosity(m/s)

x10

-6

Temperature (C)


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The wind

Wind speed has been characterized by Francis Beaufort, who

was looking for method to characterized the wind practically.

So, wind can be estimated with the surface of the sea

Beaufort scale goes from 0 to 12 bft.


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Force 6 and 7 : Warning for small

craft

Force 8 and 9 : gale warning

Force 10 and 11 : storm warning Force 12 : hurricane force wind

warning


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Beaufort scale

Bft Description Limite of wind speed Pdyn

[knots] [m/s] [km/h] [kg/m]

0 Calm


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Wind speed (2)

Wind exerts a pressure on the vessel

The pressure depends on the force :

0

10

20

30

40

50

60

70

80

90

0

5

10

15

20

25

30

35

0 2 4 6 8 10 12

Dynamic

pressure(kg/m)

Windspeed(m/s)

Wind force (bft)

Wind speed

Dynamique pressure


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Sea state

The sea state depends on the wind,

but also on the fetch (the distance

on which the wind blows) and on

the duration.

Difference between wave from the

wind and swell

Wave from the wind : the waves

present when the wind is blowing

Swell : waves which continue

without wind (the wind changes or

they leave the wind area).

We can have cross swells

(attention to interference)


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Sea state (2)

CodeWave Height

(meters)Characteristics

0 0 Calm (glassy)

1 0 to 0.1 Calm (rippled)

2 0.1 to 0.5 Smooth (wavelets)

3 0.5 to 1.25 Slight

4 1.25 to 2.5 Moderate

5 2.5 to 4 Rough6 4 to 6 Very rough

7 6 to 9 High

8 9 to 14 Very high

9 Over 14 Phenomenal

Sea state :


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Volumes and weights

Register ton : 100 ft = 2.83m

Gross Register Tonnage or Gross Tonnage (GRT or GT) : a

way to calculate the volume under the deck, with a formula.

Cost following the GT, so architect try to decrease it.

Net Register Tonnage : GTspace occupied by crew,

navigation and propulsions equipment, work stations, ballast.

Can not be less than 30% of GT.

Administrative values


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Coefficients

To characterize the shape

Waterline coefficient : ratio

waterplane area and rectangular

plane.

Midship section coefficient :

ratio midship section and thearea bounded by B and T

MldPP

W

W

BL

AC

Mld

M

M

BT

AC


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Coefficients (2)

Block coefficient CB: ratio underwaterbody and the rectangular block bounded

by LPP, BMldand T.

Prismatic coefficient Cp: rationunderwater volume and volume formed

by the midship section and Lpp. The

smallest Cp= smallest power needed

Ship type Cb Speed (kts)

Barge 0.9 5-10

Bulk carrier-Tanker 0.80-0.85 12-17

General cargo 0.55-0.75 13-22

Container ship 0.5-0.7 14-26

Ferryboat 0.5-0.7 15-26

TBL

VolumeC

MldPP

B

MPP

P

AL

VolumeC


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Curve of area

Representation of the

surface of the section,

in function of the

frames

Give an idea of the

distribution of the

volume

Area(m)

Position of the frame (m)


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Bonjean curves

Curves representing the area

of the sections in function of

the height

With the Bonjean curves, it is

possible to calculate (with

Simpsons rules) the volume of

the hull for each draft and each

trim

And also KB and LCB


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Bonjean curves (2)

Example

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 1 2 3 4 5 6

Height(m)

Section area (m)

Fr(-3m)

Fr(-1.2)

Fr(1.2)

Fr(2.4)

Fr(4.8)

Fr(8.4)

Fr(12)


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Hydrostatics

Characteristics of the hull are given by the

hydrostatics.

Datas for different trims

D/BASE DEXT DISPLT TPCM MCT/CM LCB LCF KMT KML KB

(m) (m) (t) (t) (t.m) (m) (m) (m) (m) (m)

0.1 0.2 1.05 0.22 0.366 20.564 20.777 1.216 1571.58 0.057

0.2 0.3 4.55 0.46 0.791 21.304 21.689 2.163 785.46 0.133

0.3 0.4 10.38 0.7 1.186 21.655 22.008 3.244 517 0.201

D/BASE VOLUME WL Area BMT BML WT.SURF. MID.AREA CB CW CP

(m) (m3) (m2) (m) (m) (m2) (m2) (-) (-) (-)

0.1 1.01 21.5 1.159 1571.525 30.14 0.03 0.2206 0.4677 0.7684

0.2 4.39 44.46 2.031 785.331 55 0.17 0.2743 0.5556 0.6265

0.3 10.02 67.18 3.044 516.797 79.68 0.41 0.2682 0.5392 0.5924


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Hydrostatics (2)

Also, graphically:


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Flotation

Attention will be confined to static behaviour, i.e. conditions

applying when the ship is still.

Generally, it is the change from one static condition to anotherthat will be of interest and so it is convenient to imagine any

movement occurring very slowly.

Dynamic behaviour, involving time, motion and momentum.


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Flotation

The mass density of a fluid p, is the mass of the fluid per unitvolume.

The weight density w, of a fluid is the weight of the fluid per

unit volume.

In SI units, w = pg so that, if p is in kg/m3

, w is innewtons/m3. Since they vary with pressure and temperature,

the values must be related to a standard condition of pressure

and temperature. The former is normally taken to be one

atmosphere, 105Pa = 1 Bar and the latter sometimes 15 C

and for water sometimes 4 C when its density is a maximum.


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Definitions

Material Massdensity,

p(kg/m3)

Fresh water (standard) 1000

Fresh water (British

preferred value)

996

Salt water 1025

Furnace fuel oil 947

Diesel oil 841

Petrol 697Steel 7689

Mahogany 849

Air 1.293

c p c P c P

0 999.79 10 999.59 20 998.12

1 999.79 11 999.49 21 997.92

2 999.89 12 999.40 22 997.72

3 999.89 13 999.30 23 997.43

4 999.89 14 999.10 24 997.24

5 999.89 15 999.00 25 996.94

6 999.89 16 998.91 26 996.75

7 999.79 17 998.71 27 996.458 999.79 18 998.51 28 996.16

9 999.69 19 998.32 29 995.87

30 995.57

Mass densities for fresh water


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ARCHIMEDES' PRINCIPLE

This states that when a solid is immersed in a liquid, itexperiences an upthrust equal to the weight of the fluid

displaced.

Thus, the tension in a piece of string by which a body is

suspended, is reduced when the body is immersed in fluid byan amount equal to the volume of the body times the weight

density of the fluid; a diver finds an article heavier to lift out of

water than under it, by an amount equal to its volume times the

weight density of water


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Definitions

This upthrust is called the buoyancy of the object.

If, by chance, the body has the same weight density as the fluid,

the upthrust when it was totally immersed would be equal to its

weight; the diver would find the object to be apparently

weightless.

If the body were to have a smaller weight density than the fluid,

only sufficient of the body to cause an upthrust equal to its weightcould be immersed without force; if the body is pushed further

down the buoyancy exceeds the weight and it bobs up, like a

beach ball released from below its natural position in the sea.


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Definitions

This leads to a corollary of Archimedes' principle known as theLaw of Flotation.

When a body is floating freely in a fluid, the weight of the body

equals the buoyancy, which is the weight of the fluid displaced.

The buoyancy of a body immersed in a fluid is the vertical

upthrust it experiences due to displacement of the fluid.


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Definitions

The body, in fact, experiences all of thehydrostatic pressures which obtained

before it displaced the fluid.

The buoyancy is the resultant of all of the

forces due to hydrostatic pressure on

elements of the underwater portion.

Now, the hydrostatic pressure at a point in

a fluid is equal to the depth of the point

times the weight density of the fluid, i.e. it

is the weight of a column of the fluidhaving unit cross-section and length equal

to the depth of immersion, T

p = Tw

Resultant = \buoyancy j A

Txw


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Definitions

Let us examine the pressure distribution around a rectangular

block a x b x c floating squarely in a fluid at a draught T.

The pressures on the vertical faces of the block all cancel out

and contribute nothing to the vertical resultant; the hydrostaticpressure at the bottom face is Tw and so the total vertical

upthrust is this pressure multiplied by the area:

upthrust = (Tw)ab


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Vertical movement

The figure shows the forces acting upon afloating body which are

- The weight, vertically downwards, which

may be taken for static considerations as

acting as if it were all concentrated at the

centre of gravity, as for any rigid body;

- The buoyancy, vertically upwards, which

may be assumed concentrated at the centre of

buoyancy, which is the centre of volume of

the underwater shape.It must be made clear that when the ship is

still, the weight and buoyancy forces must

act in the same straight line BG, otherwise a

couple would act upon the ship, causing it tochan e its attitude.


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Definitions

What happens when a small weight is placed on the vertical line

through BG?

The ship undergoes a parallel sinkage having a buoyancy W andthe centre of buoyancy B moves towards the addition by an

amount BB. Taking moments about B

WBb = ( + W)BB

BB= WBb/( +W)


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Definitions

In the same way, the ship has a new centre

of gravity. Taking moments about G

Stability Lecture 1

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