Download - 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
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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