船舶原理4.7 - 4.8 Damage Stability & Free Surface Correction

SINE CORRECTION
(Due to vertical changes in G)
When the ship heels over, the center of buoyancy, B, shifts. The shift creates a distance or “moment arm”. MT
The KG value for the ship is given… this is the ACTUAL G position from the keel...
MT
φ
B1
KG forms a similar triangle that gives the value for the SINE correction
φ
Z0 B1
G0Z0 = Moment Arm
For values taken from the Cross Curves of Stability, G0 is at thwenku.baidu.com keel...
MT
φ
B1
Z0
G0Z0 = Moment Arm
This value is recorded as G0Z0, the Initial Moment Arm.
This correction factor is called:
PERMEABILITY = AVAILABLE VOLUME TOTAL VOLUME
Some typical factors are: Watertight compartment (warship) Watertight compartment (merchant)95% Accommodation spaces Machinery spaces Dry cargo spaces Bunkers, stores, cargo holds
97% 95% 85% 70% 60%
Example: A cargo hold with dimensions of l=50ft, w = 30ft, h= 20ft is completely flooded. Determine the volume of the space and the corrected flooded volume:
Original draft
A flooded compartment does not fill completely with water, however. Compartments contain equipment, furniture, structural components, and cargo. A correction factor must be added to the volume of the compartment to accurately reflect conditions...
Cosine Corr = GvGT cosφ
The final moment arm, GTZT, is the correct moment arm
φ Zv GT ZT
GTZT = GvZv - GvGT cosφ
Volume = 50 ft x 50ft x 20ft = 50,000ft3 Flooded volume = Volume x permeability Flooded volume = 50,000ft3 x 60% Flooded volume = 30,000ft3
...Once the volume is corrected, the determination of the new “G” and changes and list and trim are computed as previously discussed
determines the value based upon the change in parallel sinkage that results.
Original draft
The change in the draft reflects the amount of buoyancy lost. The ship sinks until the available submerged volume is again equal to the ship’s displacement
The vessel’s draft will increase because an amount of the buoyancy was lost...
Lost buoyancy considers the amount of buoyancy “lost” as a result of the hole, and
The Added Weight Method considers the resulting flooding as though it was a
weight added to the ship. This is the method that will be used in this course.
(Due to transverse Changes in G)
MT
φ
Zv
MT
φ
Zv G
TCG
T
The red line indicates the COSINE Correction factor for a transverse change in G.
φ Zv GT ZT
Note that GvGT is the TCG value and is the hypotenuse of this correction triangle...
Section 4.7 - 4.8 Damage Stability & Free Surface Correction
When a vessel is damaged, creating a a gap or hole in the hull, water will breech the ship. This results in: • Increase in draft • Change in trim • Permanent angle of list
Z0
Sin φ = opp hyp
Opp =correction factor Hyp = KG
Sine Correction factor = KG Sin φ
MT
φ
B1
Z0 Sin Correction = KG Sin φ
MT
φ
Zv B1
Z0
GvZv = G0Z00 - KG sinφ
COSINE CORRECTION
The result of this flooding can be determined two ways: • Lost Buoyancy Method • Added Weight Method
Consider a vessel that has been damaged such that a portion of the bottom is now open to the sea...