fse on ship stability
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FREE SURFACE EFFECT ON SHIP STABILITY
Submitted by
G. Vinod kumar M100 420 CE
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LAW OF FLOATING BODIES
A floating object has the property of buoyancy A floating body displaces a volume of water equal in weight to
the weight of the body. A body immersed (or floating) in water will be buoyed up by a
force equal to the weight of the water displaced.
STABILITY REFERENCE POINTS
CL
M
G
B
K
etacenter
ravity
uoyancy
eel
CENTER OF BUOYANCY (B)
The centroid of the underwater volume of the ship is the location where the resultant buoyant force acts.
B
WATERLINERESERVE BUOYANCY
B1
B “B” FOLLOWS THE WATERLINE
B
WLWL
B
WL
B
WL
B
WL
B
CENTER OF GRAVITY (G)
Point at which all weights could be concentrated. Center of gravity of a system of weights is found by taking
moments about an assumed center of gravity, moments are summed and divided by the total weight of the system
G moves towards the weight addition. G moves away from the weight removal.
GGGGGGG1
KG1
KGo
G
META CENTER (M)
The intersection of vertical lines through the center of buoyancy of a floating body when it is at equilibrium and when it is floating at an angle.
The location of the metacenter is an indication of the stability of a floating body.
the metacenter will change positions in the vertical plane when the ship's displacement changes.
“M” MOVES OPPOSITE OF “B”
LINEAR MEASUREMENTS IN STABILITY
CL
M
G
B
K
GM
KG
BM
KM
METACENTRIC HEIGHT
HEIGHT OF METACENTER
METACENTRIC RADIUS
HEIGHT OF GRAVITY
OVERALL STABILITY
The horizontal distance between the positions of the ship’s displacement vector and the buoyant force vector help determine stability.
The relationship changes when a ship is heeled by an external moment.
External forces :- wind, wavesExternal moment:- It can be caused by wind pushing on one side of the vessel and
water resisting the motion on the other side. Each distributed force can be resolved into a resultant force
vector. The wind acts above the waterline and the water resistance acts below the waterline.
Continued…..
The two forces create couple because they are equal in magnitude, opposite in direction, and not aligned.
The couple causes rotation or heeling. The vessel will continue to rotate until it returns to Static
Equilibrium.Internal forces :- The resultant weight , The resultant buoyancy Internal Forces create a Righting Moment to counter the
Upsetting Moment of the External Forces.
Internal Righting Moment
The perpendicular distance between the Weight and the Buoyancy Force vectors is defined as the RIGHTING ARM (GZ).
The moment created by the resultant Weight and the resultant Force of Buoyancy is defined as the RIGHTING MOMENT (RM). It may be calculated by
Where: RM is the internal righting moment of the ship s is displacement of the ship in Fb is the magnitude of the resultant buoyant force GZ is the righting arm
RM GZ GZ F b
M
ZG
B B1
CL
OVERALLSTABILITY
RM = GZ x Wf
FINAL DISPLACEMENT
CURVE OF STATICAL STABILITY
Shows the Heeling Angle () versus the righting arm (GZ). Assumes the vessel is heeled over quasi- statically in calm water.
Continued…..
Predictions made by the Curves of Intact Statical Stability are not accurate for dynamic seaways because additional external forces and momentum are not included in the analysis.
Since stability is a function of displacement, there is a different curve for each displacement and KG! These are called the Cross Curves.
RANGE OF STABILITY
The range of angles for which there exists a positive righting moment.
The greater the range of stability, the less likely the ship will capsize.
If the ship is heeled to any angle in the range of stability, the ship will exhibit an internal righting moment that will right the ship if the external moment ceases
DYNAMICAL STABILITY The work done by quasi-statically rolling the ship through its
range of stability to the capsizing angle. It can be calculated by the the product of the ship’s displacement
with the area under the Curve of Intact Statical Stability. Does not account for the actual dynamics, because it neglects
the impact of waves and momentum.
The largest Static Moment the ship can produce. Calculated by multiplying the displacement of the vessel times
the maximum Righting Arm The larger the Maximum Righting Moment, the less likely the
vessel is to capsize. The angle of inclination where the maximum Righting Arm occurs Is called angle of maximum righting arm.
MAXIMUM RIGHTING MOMENT
Continued…..
MEASURE OF STIFINESS The initial slope of the intact statical stability curve indicates the
rate at which a righting arm is developed as the ship is heeled over. This slope is GM.
A steep initial slope indicates the rapid development of a righting arm and the vessel is said to be stiff. Stiff vessels have short roll periods and react strongly to external heeling moments.
A small initial slope indicates the slower development of a righting arm and the vessel is said to be tender. Tender vessel have longer roll periods and react sluggishly to external heeling moments.
FREE SURFACE EFFECT
A free surface is fluid that is allowed to move freely, such as water in a partially filled tank. As the ship lists, the fluid in the tank moves.
The fluid movement acts like a weight shift, causing the center of gravity of the fluid to move which causes the ship's center of gravity to shift in both the vertical and horizontal directions
The effect of the vertical shift is negligible at small angles and is discounted, but the horizontal (transverse) shift of the center of gravity causes a decrease in the righting arm.
The distance the center of gravity would have to rise to cause a reduction in the righting arm equivalent to that caused by the actual transverse shift is called the Free Surface Correction (FSC). he righting arm (GZ).
The position of this new center of gravity is called the "virtual" center of gravity (Gv) and for GM effective meta center.
FREE SURFACE EFFECT
G
B
M
G
B
M
B1
G2G
B
M
B1
G2G
B
M
B1
G2
B1
G2G
B
M
B1
G2
G
B
M
B1
G2
ZZ2
Z3G3
B
M
B1
G
G3
GG3
FREE SURFACE CORRECTION
GG3 =B3 x L
12 x 35 x Wf
B = BREADTH OF COMPTL = LENGTH OF COMPTWf = SHIP'S DISPLACEMENT
FREE SURFACE CORRECTION
= MOMENT OFINERTIA
=SHIP'S DISPLACED VOLUME
STATIC EFFECTS
Virtual rise in center of gravity. Smaller range of stability. Smaller righting arm. Small angle at which maximum righting arm occurs. exaggerated list and trim if the ship is listing or trimming.
DYNAMIC EFFECTS
It has nothing to do with the dynamic effects of the water rushing back and forth.
This effect is also detrimental but is not described by the free surface correction.
EXAMPLES Fire engine with out baffles. Baffles are a good way to minimize the dynamic effects of free
surface.
CASE STUDY
MAIN PARTICULARSLENGTH O.A. 97.054 m
LENGTH W.L 96.839 m
LENGTH B.P. 96.839 m
BEADTH MLD. 33.3 m
DRAFT 3.7 m
DISPLACEMENT 11080 T
GENERAL PARTICULARSNAME OF SHIP SURYA PRATHAMA
TYPE PONTOON
TONNAGEGROSS TONNAGE 18347.72 T
NET TONNAGE 1570.23T
MODELLING OF THE SHIP
PLAN AND PROFILE VIEW
ISOMETRIC VIEW
TANK PLAN
LOADING CONDITIONS
10 % ARRIVALLight Weight = 3474 TTotal weight =11076.848T DISP = 11076.910 T LCG = -0.468 m LCB = -0.467 m LCF = -1.149 m TPC = 31.083 T MTC = 222.587 m-t TRIM = -0.001 m MEAN DRAFT = 3.699 m DRAFT FP = 3.700 m DRAFT AP = 3.699 m
VCG = 2.655 m GMT UNCORR. = 24.854 m FREE SURF. = 0.779 m GMT CORR. = 24.076 m
FSM =8623.68T-m
Intact stability curveCOND: 10000000002 10% ArrivalDISPL= 11076.91 LCG= -0.47 VCG= 2.66
0 15 30 45 60 75 90
0.0
7.5
15.0
22.5
30.0
GZ IN METRES
ANGLE IN DEGREES -> Starboard
GZ
GMT
Light Weight = 3474 TTotal weight =11068T DISP = 11068.746 T LCG = -0.469 m LCB = -0.469 m LCF = -1.149 m TPC = 31.083 T MTC = 222.587 m-t TRIM = -0.001 m MEAN DRAFT = 3.697 m DRAFT FP = 3.697m DRAFT AP = 3.696 m
VCG = 2.509 m GMT UNCORR. = 25.017 m FREE SURF. = 0.591 m GMT CORR. = 24.426 m
FSM =6539.36T-m
100% Fully Loaded Departure
Intact stability curveCOND: 10000000001 100% Fully Loaded DepartureDISPL= 11068.75 LCG= -0.47 VCG= 2.51
0 15 30 45 60 75 90
-7.5
0.0
7.5
15.0
22.5
GZ IN METRES
ANGLE IN DEGREES -> Starboard
GZ
GMT
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