Stability Lecture3

8/3/2019 Stability Lecture3

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Stability :longitudinal stability

Stability while underway

Dynamic stability

Ship Theory


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Stability while underway and

dynamic stability

Up to now and in general in hydrostatics, we

consider that :

The boat is not underway

T e water is ca m

The external forces are apply slowly

Here we will see what happens when these

assumptions are not verified.


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Degrees of freedomA boat has 6 degrees of freedom.

3 translations : Surge (longitudinal)

Sway (transverse)

3 rotations: Roll (longitudinal)

Pitch (transverse)

eave vert ca Yaw vertical


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Degrees of freedom Translational movements are a-periodic and uncontrolled and

caused by waves. Ship does not come back at its originalposition

Rotational movements are periodic and the ship comes back

.

Underway, a ship will make combination of these movements.

So, external forces change all the time in sea


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Ship in rough sea Because waterplane changes

all the time, stability also will

change.

In function of the waves

waterplane change:

Increase when crest in

the middle

Decrease when trough inthe middle

In case of quarter beam sea, much

more complex


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ExampleContainer ship :

Length WL : 192.9 m

Beam WL : 32.2 m

Draft : 10.56 m

Diplacement : 34700 t CB : 0.511

CP : 0.544


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Example : wave position In function of the sea, the waterplane will change..

Most extreme case : wave lenght = length of the ship

2

3

4

-4

-3

-2

-1

0

1

0 20 40 60 80 100 120GZ(m)

Heeling angle ()

Still water

Trough in the middle

Crest in the middle

So, stability changes all

along the time !

Wave heigth : 8.717 m

Wave length : 206.25 m


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Example : wave height If the wave height changes

Attention : not realistic waves, only the height change (not theperiod)

3

-4

-3

-2

-1

0

1

2

0 20 40 60 80 100 120

GZ(m)

Heeling angle ()

Still water

Wave height : 2 m

Wave height : 4 m

Wave height : 6 m

Wave height : 8 m

Wave height : 10 m


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Other problems Stability varies during the movement, and can

become negative

Resonance p enomenon can ea to capsize

Impact of wave can cause extreme rolling


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Broaching Broaching is a type of ship motion instability

which is exhibited in the horizontal plane by a

sudden large yaw from the initial course. Theresulting Transverse forces acting on the shipsunderwater body can introduce large heelingmoments.

It may happen with big wave length, in case of stern quartering seas.

It is due to the movement of

particle of the waves :


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Broaching

The crest is on thestern and the bow is

in a trough

change of yaw,creation of a turning

moment

If rudder is not bigenough : broaching


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Longitudinal stabilityLength > beam

Because thee length of the ship is greater than the beam,the moment of inertia of the watetline is also much greaterlongitudinally than laterally.

So, no pro em o ongitu ina sta i ity

Longitudinal stability, thus, has no direct relationship to theships safety. Therefore, there is also no need to calculate or

evaluate the ships longitudinal stability.

But


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Center Of Flotation The ships trim around the centre of floatation.

In case of a barge with rectangular shapes, the. ,

1 m, bow will rises out of the water of 0.5 mand stem will immerse of 0.5 m.

So COF has a direct relationship to draft andtrim


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Moment to change trim To change the trim, a longitudinal moment

should be exerted.

T is moment can e create y a c ange inthe longitudinal direction of some weight.

How to determine it without the 3D model

and a stability software?


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Moment to change trim (2)Displacement 139,097 tonne

Volume 135,704 m^3

Draft to Baseline 1,5 m

Immersed depth 1,5 m

Lwl 30,208 m

Beam wl 4,342 m

WSA 168,439 m^2

Max cross sect area 6,365 m^2

Waterplane area 100,806 m^2

C 0 706

Serie 60

Cb 0,69

Cm 0,978

Cwp 0,769

LCB from zero pt 0,476 m

LCF from zero pt 0,022 m

KB 0,791 m

KG 0 m

BMt 0,961 m

BMl 37,276 m

GMt 1,751 m

GMl 38,066 m

KMt 1,751 m

KMl 38,066 m

Immersion (TPc) 1,033 tonne/cm

MTc 1,709 tonne.m

RM at 1deg =

GMt.Disp.sin(1) 4,251 tonne.m

Moment to change trim


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Moment to change trim (3) To calculate the change of trim :

With

p the transferred weight, a = the distance over which weight is

MTc

ap

trim

=

p the loaded weight, a = the distance from the pivot (COF) to thearea where the weight has been loaded

p = unloaded weight, a=distance from the place where the weightwas located to COF.

and MTc the moment to change trim.

Attention, it is the change of trim and not the trim.


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How to calculate the trim Another way to write it (with the equilibrium

of the moment):GB

Trimlongi

=

Or, we can calculate the difference of LCB and

LCG :

c

=

MTctrimLCGLCB


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Trim Remark :

Distribution of trim around the COF.

foreaft TTtrim =

So :

And :

length

LCFtrimtotalTrimaft

=

aftfore trimtrimtotalTrim =

Stability Lecture3

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