STABILITY THEORY III
Author : Mr. Charumathy Sreeraman
TABLE OF CONTENTS :
| Effect of cargo shifting on GZ | GZ curve transverse shift | GZ curve changing the trim | GZ curve
decreasing the beam | GZ curve decreasing the freeboard | GZ curve decreasing the FSC | GZ curve
flooding | GZ curve ice accretion | GZ curve in neutral condition | GZ curve in stable condition | GZ
curve in unstablel condition | GZ curve increase in draught | GZ curve increasing the beam | GZ
curve increasing the freeboard | GZ curve increasing the FSC | GZ curve timber cargo |
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During a course of a voyage, the bulk cargo, originally trimmed level within a hold, shifts
to one side. Describe with the aid of diagrams, the effect that this shift of cargo would have
on the curve of statical stability.
(1) Solid bulk cargoes are liable to shift when the angle of heel due to heavy weather rolling
exceeds their angle of repose.
(2) When the cargo shifts, the vessels develops a heel angle and the vessel roll about the
angle of list.
(3) Subsequent rolling will result in the ship being heeled to a greater angle of heel on the
listed side that will lead to further shift of cargo.
(4) When a solid bulk cargo shifts, a large chunk of cargo is lying off the centre line which
has the effect of a weight added at a height.
(5) The following diagram represents the shifting of cargo within a hold.
(6) It can be seen that a wedge of grain has moved from g to g1.
(7) Thus G moves towards the added weight and away from the centre line to a new position
G1
(8) This has two effects on the vessel’s righting lever GZ.
(9) A small vertical component causes the G to rise from G to GV resulting in the increase of
he KG and decrease in GM.
(10) A large horizontal component which causes the ship’s centre of gravity to move off
centre line - G to GH causing list.
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Vertical shift of G
Loss of GZ to vertical
comp = GGV x Sinθ
Horizontal shift of G
Loss of GZ to horizontal
comp = GGH x Cosθ
11) The original GZ will be reduced as a result of both components of the shift of
G to give the final condition after the shift of cargo has taken place.
12) If the vessel has sufficient stability then it would remain in a listed, yet stable
condition.
13) Provided that the rolling motion and cargo shift does not take the angle of heel
beyond the point max of G, it will be harder to heel the ship further and
subsequent shifts of cargo will diminish
14) The following diagram shows the effect of shift on solid bulk cargo on vessel’s
statical stability.
.
16) From the above diagram it can be seen that:
a) GM is reduced due to increase in KG.
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b) Angle of deck edge immersion very little change due to little
decrease in freeboard. However angle of deck edge immersion can be easily reached
on the heeled side.
c) Area under the curve (dynamical stability) is reduced due to reduction in the GM (curve
is lowered).
d) Reduction in the residual stability.
e) Reduction in the range of stability- from list angle to angle of vanishing stability
f) Maximum residual GZ value reduced.
g) Angle of maximum GZ value – small reduction.
h) Heel arm produced as a result of horizontal shift of G. List depends on the values of GM
and horizontal shift of G.
i) Angle of loll - there could be angle of loll if the GM were to become negative.
Describe with the aid of a labeled sketch the following initial stability conditions, when
applied to a freely floating vessel in the upright condition.
STABLE CONDITON
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θde
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NEUTRAL CONDITION
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UNSTABLE CONDITION
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Describe with the aid of sketches, the effects on a ship’s curve of statical stability for the
following conditions:
Increasing the beam:
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1) From the above diagram, it can be seen that with increase in the beam, the outward
movement of B to B1 is much greater. This creates a larger value of BM and effectively
increases the GM of the vessel.
2) The following figures illustrate two GZ curve, one for narrow beam and other for wider beam
vessel.
3)
a)
b)
c)
d)
e)
f)
g)
From the above diagram, it can be seen that,
GM increases because of increase in beam.
Angle of deck edge immersion reduces because of the freeboard / half beam width ratio,
Area under the curve is increased because of the increase in GM and decreased because of
decreased angle of deck edge immersion. There will be an over all increase.
Maximum GZ value is increased.
Angle of maximum GZ is increased.
Range of positive stability increased.
No list and no angle of loll.
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Decreasing the beam:
1) From the above diagram, it can be seen that with decrease in the beam, the
outward
movement of B to B1 is much reduced. This creates a reduction in value
of BM and
effectively decreases the GM of the vessel.
2) The following figures illustrate two GZ curve, one for narrow beam and other for wider
beam vessel.
3)
a)
b)
c)
From the above diagram, it can be seen that,
GM reduces because of decrease in beam.
Angle of deck edge immersion increases because of the freeboard / half beam width ratio.
Area under the curve is reduced because of the decrease in GM and increased because of
increased angle of deck edge immersion. There will be an over all reduction
d) Maximum GZ value is decreased.
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e) Angle of maximum GZ is decreased.
f) Range of positive stability decreased.
g) No list and no angle of loll.
Changing the trim:
1) No change in the GM
2) Reduction in the angle of deck edge immersion.
3) Area under the curve is reduced due to smaller angle of deck edge immersion. The
amount of reduction depends upon the trim.
4) Range of positive stability is reduced.
5) Max GZ value is reduced.
6) Angle of maximum GZ is reduced.
7) List – None
8) 8) No angle of loll
Decreasing the Freeboard:
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1) The above figure indicates two ships of similar characteristics, having
different freeboard.
2) At angle of heel upto deck edge immersion of smaller greater freeboard ship, the curve of
statical stability will be exactly same.
3) At angles of heels beyond deck edge immersion of smaller freeboard vessel, the values of GZ
will be smaller for smaller freeboard vessel since the curve steepness does not continue any
more upto large angles of heel.
4) This is as a result of reduction in the size of water plane areas as compared to larger
freeboard vessel.
5) The following diagram illustrates GZ curve for both vessels.
6) From the above diagram it can be seen that:
i. GM remains unchanged.
ii. Angle of deck edge immersion is decreased.
iii. GZ values will be decreased at angles of heels beyond the angle of deck edge
immersion of greater freeboard vessel.
iv. Area under the curve decreased due to reduction in the angle of deck edge
immersion.
v. Range of stability is reduced.
vi. Max GZ value is decreased
vii. Angle of max GZ value is decreased.
viii. No list
ix. No angle of loll.
Increasing the freeboard:
1) The above figure indicates two ships of similar characteristics, having different freeboard.
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2) At angle of heel upto deck edge immersion of smaller freeboard ship,
the curve of statical stability will be exactly same.
3) At angles of heels beyond deck edge immersion of smaller freeboard vessel, the values of GZ
will be greater for greater freeboard vessel since the curve steepness continues upto large
angles of heel
4) This is as a result of increase in the size of water plane areas as compared to smaller
freeboard vessel.
5) The following diagram illustrates GZ curve for both vessels.
6) From the above diagram it can be seen that:
a) GM remains unchanged.
b) Angle of deck edge immersion is increased.
c) GZ values will be increased at angles of heels beyond the angle of deck
immersion of smaller freeboard vessel.
d) Area under the curve increased due to increase in the angle of deck edge
immersion.
e) Range of stability is increased.
f) Max GZ value is increased
g) Angle of max GZ value is increased.
h) No list
i) No angle of loll.
edge
Increasing the Free Surface effect
1) Free surface effect results in the virtual loss of GM.
2) Greater the FSE, greater the loss of GM.
3) The following diagram shows curve of statical stability of a vessel, one
with greater FSE than the other.
4) From the curve it can be seen that:
a)
GM is reduced.
b)
Angle of deck edge immersion remains the same.
c)
Area under the curve is decreased due to reduction in
GM.
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d)
e)
f)
g)
it
h)
Range of positive stability is reduced.
Max GZ value is reduced.
Angle of Max GZ value has a small reduction.
No angle of loll – However if the Free surface effect is very high
could result in negative GM causing the
vessel to loll over.
No list.
Decreasing the Free Surface effect
1) Free surface effect results in the virtual loss of GM.
2) Greater the FSE, greater the loss of GM.
3) The following diagram shows curve of statical stability of a vessel, one with
smaller FSE than the other.
4) From the curve it can be seen that:
a) GM is reduced.
b) Angle of deck edge immersion remains the same.
c) Area under the curve is decreased due to reduction in GM.
d) Range of positive stability is reduced.
e) Max GZ value is reduced.
f) Angle of Max GZ value has a small reduction.
g) No angle of loll – However if the Free surface effect is very high
it could result in negative GM causing the vessel to loll over.
h) No list.
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Shifting weight transversely (OR) Transverse shift of cargo (eg R-Ro units)
(OR) List due to off centre weight
1) From the above figure it can be seen that if a weight is transversely moved across the deck,
the G of the vessel moves parallel to and in the same direction as the movement of weight.
2) The righting lever is thus reduced from GZ to GHZ1 as a result of transverse shift of weight.
3) Loss of GZ = GGH x Cosθ
4) The loss of GZ will decrease as the angle of heel increases. Greatest loss being when the
vessel is upright.
5) Equilibrium is reached when the heeling arm and righting lever are equal and opposite and
the vessel tends to lie at this angle – LIST ANGLE.
6) The following diagram shows the effect on curve of the statical stability.
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7) It can be seen from the above curve that:
a) Initial GM is unchanged since only vertical movement of G will cause this to change.
b) All GZ values across the range of stability are reduced particularly at smallest angle of
heel.
c) Heel arm curve is produced as a result Horizontal movement of G.
d) Area under the curve is decreased due to losing the area under the heeling arm curve.
e) Since the dynamical stability is reduced, less work is required by external forces to heel
the ship further on the listed side.
f) Range of positive stability is reduced. It is only from list angle to angle of vanishing
stability.
g) No change in the angle of deck edge immersion.
h) Maximum GZ value reduced.
i) Angle of Max GZ is decreased.
j) No angle of loll
k) List angle present. Angle is at the point of intersection of heeling arm curve and GZ
curve.
Increase in draught:
(Assuming KG remains the same)
1)
2)
3)
4)
5)
6)
7)
8)
No change in the GM
Angle of deck edge immersion is reduced due to reduction in the freeboard.
Area under the curve is reduced due to reduction in the angle of deck edge immersion.
Reduction in the range of positive stability.
Reduction in the Max GZ value.
Angle of Max GZ value reduction.
No loll
No list.
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Departure and Arrival condition curve on the same axis. Explain the reasons
for the differences between the two curves
OR
During the course of a voyage the stability of a vessel may change. State the
likely causes of such a change and show the effect this has on the vessel’s GZ
curve.
It is assumed that during the voyage oil and water are consumed from the double bottom and
other low level tanks reducing the GM and the reduction of weight causes a slight increase of the
freeboard.
1) GM decreases.
2) Angle of deck edge immersion increases due to increase in freeboard.
3) Area under the curve decreases due to reduction in the GM and increases due to increased
angle of deck edge immersion. The overall effect is usually a reduction of area. Displacement
reduces and hence the dynamical stability will almost certainly decrease.
4) Range of stability decreases duet to reduced GM and increases due to increased angle of deck
edge immersion. The overall effect is usually a reduction of range.
5) Max GZ value decreases.
6) Angle of max GZ decreases.
7) No angle of loll
8) No list.
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Reasons:
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Angle of loll condition due to small negative GM.
1) Angle of loll is caused due to initial GM being negative.
2) The following curve represents the statical stability of the vessel with a small initial negative
GM.
3) From the curve it can be seen that
a) GM is negative in upright condition.
b) When heeled to a small angle of heel, a lever is produced which acts as a capsizing
lever.
c) Vessel continues to heel further and will now rest at an angle of loll.
d) No righting lever produced at angle of loll.
e) If vessel continues to heel beyond angle of heel, the a positive righting lever is
produced.
f) Area under the curve is initially is negative and then becomes positive. However
again becomes negative usually at a relatively small angle.
g) Range of stability is small.
h) Range of stability is from loll angle to angle of vanishing stability.
i) Max GZ value is small.
j) Angle of deck edge immersion is the same as the vessel with positive stability
floating at this draught.
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Lowering a KG
1)
2)
3)
4)
5)
6)
7)
8)
GM is increased as the KG is decreased.
Angle of deck edge immersion remains the same.
Area under the curve is increased
Range of stability is increased as the GM is increased.
Maximum GZ value is increased.
Angle of max GZ value has a small increase.
No angle of loll
No list
Increasing the KG
1)
2)
3)
4)
5)
6)
7)
8)
GM is reduced due to increase in KG
Angle of deck edge immersion remains the same
Area under the curve is reduced due to reduction of GM.
Range of positive stability is reduced.
Max GZ value is reduced.
Angle of max GZ value has a small reduction.
No angle of loll
No list.
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GZ curve for vessel with a ZERO GM affected by a rise in the KG and
Reduction in the KG
1) The following diagram illustrates three curves, one with zero GM, curve showing the effect
on zero GM curve when KG is increased and the other when the KG is reduced.
2) When the GM is zero the vessel is in neutral condition. A further heel will produce righting
lever and subsequent positive stability.
3) When the KG is increased from a condition where initial GM is zero,
a) the initial GM is reduced giving negative GM (-0.2m in this case).
b) Range of stability reduces – from angle of loll to angle of vanishing stability.
c) Area under the curve decreases.
d) Max GZ value decreased
e) Angle of max GZ value decreases.
f) Vessel will be in unstable condition and will continue to heel until she rests at angle
of loll.
g) No change in the angle of deck edge immersion.
h) No list condition.
4) When the KG is decreased from a condition where initial GM is zero, then
a) the initial GM increases producing positive GM (0.2m in this case)
b) Range of stability is increased.
c) Area under the curve increases
d) Max GZ
e) Angle of max GZ increases
f) No angle of loll
g) No list
h) Angle of deck edge immersion remains the same.
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Curve with FSE compared to the curve without FSE
1)
2)
3)
4)
5)
6)
7)
GM is reduced.
Angle of deck edge immersion remains the same.
Area under the curve is reduced.
Range of stability is reduced.
Max GZ value is reduced.
Angle of Max GZ is reduced.
No angle of loll. However if the FSE is much higher then it could result in negative GM and
subsequent angle of loll.
8) No list
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Stiff Ship:
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Tender Ship:
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A vessel operating in severe winter conditions may suffer from ice
accretion on decks and superstructure which is not symmetrical.
Describe the effects of this on the overall stability of the vessel making a
particular reference to the curve of statical stability.
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Vertical shift of G
Loss of GZ to vertical
comp = GGV x Sinθ
Horizontal shift of G
Loss of GZ to horizontal
comp = GGH x Cosθ
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12) It can be seen from the above curve that due to unsymmetrical ice accretion:
a) GM is reduced due to increase of weight due to ice high on the ship.
b) Angle of deck edge immersion – Very little change because of freeboard decreased a little
due to extra weight of ice. However it is easily reached on the heeled side.
c) Dynamical stability or the area under the curve is reduced due to reduced GM (curve is
lowered) and reduced due to heeling arm curve (area above curve). Overall effect area under
the curve largely reduced making the ship less able to resist heeling by external force.
d) Reduction in the maximum GZ. Also all values of GZ across the range of stability are
reduced.
e) Angle of maximum GZ values – small reduction.
f) Range of stability greatly reduced – from List angle to angle of vanishing stability.
g) No angle of loll. However vessel could loll over is the GM was to be negative.
h) List depends upon the value of GM and the horizontal shift of G.
A vessel is involved in a collision which results in side damage and substantial
flooding of a large off centre compartment on the starboard.
With the aid of one or more sketches of the vessel’s curve of statical stability,
show the effects of such side flooding on the damage stability of the vessel.
1) In the event of bilging a side compartment there are two conditions affecting the ship viz.,
a) The vessel will develop a list to the bilged side (in this case starboard side)
b) The sinkage will increase to compensate for the loss of underwater volume. Hence the
freeboard reduces.
2) The following curve of statical stability illustrates the effect of bilging a side compartment.
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3) From the above curve it can be seen that,
a) A heel arm is developed due to listing moment.
b) Initial GM is unchanged as there is no vertical rise of G.
c) Equilibrium is reached when the heeling arm and righting lever are equal and
opposite and the vessel tends to lie at this angle – LIST ANGLE.
d) All GZ value across the range of stability is reduced because of HEEL ARM and
reduction in GZ curve due to decrease in freeboard.
e) Loss of GZ is given by GGH x Cosθ.
f) Loss in GZ is reduced as the angle of heel increases.
g) Area under the curve (Dynamical stability) is reduced due to HEELARM and further
reduced due to the reduction in freeboard
h) Range of stability is reduced , more so due to reduction of freeboard.
i) Angle of deck edge immersion remains unchanged with list BUT will decrease due
to decrease in Freeboard. Due to loss in dynamical stability, less work is required
by the external force to reach this angle easily on the listed side.
j) No angle of loll
k) Max GZ reduced
l) Angle of max value of GZ is reduced.
A vessel loads a packaged timber cargo on deck such that there is an increase in
the vessel’s KG and an effective increase in freeboard. Using a sketch show the
effects of loading this cargo on the vessel’s GZ curve.
Loading timber on deck has the two major effects on ship viz.,
1) Increase in KG due to deck cargo.
2) Increase in freeboard as the stack of timber cargo on deck acts as additional reserve
buoyancy.
3) The following diagram has two GZ curves, one indicating the GZ curve for vessel prior
loading timber deck cargo and the other after loading timber cargo on deck.
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4) It can be seen from the above curve that
a) GM is reduced due to the increase in the KG of vessel.
b) Area under the curve (dynamical stability) is reduced initially reduces but increases due to
the effect of the extra freeboard as the angle of heel increases. The overall effect is probably
an increase.
c) However it depends on the relative effects of the reduced GM against the increased
freeboard.
d) Range of stability increases.
e) Maximum GZ value could be an increase or a decrease. It depends on the relative effects of
the reduced GM against the increase in freeboard.
f) Angle of maximum GZ value increases.
g) Angle of loll. If GM becomes negative, there could be well be an angle of loll.
h) There is no list developed.
Show how a curve of statical stability produced using ordinary KN values differs
from a curve produced using KN values labeled Free Trim
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TABLE OF CONTENTS :
| Effect of cargo shifting on GZ | GZ curve transverse shift | GZ curve changing the trim | GZ curve
decreasing the beam | GZ curve decreasing the freeboard | GZ curve decreasing the FSC | GZ curve
flooding | GZ curve ice accretion | GZ curve in neutral condition | GZ curve in stable condition | GZ
curve in unstablel condition | GZ curve increase in draught | GZ curve increasing the beam | GZ
curve increasing the freeboard | GZ curve increasing the FSC | GZ curve timber cargo |
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