Ship tecnic Sharif university Lecture 5
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Transcript of 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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SHIPS STABILITY VARIATIONS
FREE LIQUID AREA
P1
W0 L0
C0
G0
m
M Moment liquid
M Moment upserting
P1
C1W1
L1
Q
Mcargo
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SHIPS STABILITY VARIATIONS
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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