Stability – I : Chapter 6

  1. In a vessel of 8800 tonnes displacement and KG 6.2m, 200 tonnes of cargo was loaded in the lower hold 1.7m above the keel. Find the final KG.
Solution:

Given:-

Weight = 8800t,
Original KG =6.2m,
Cargo loaded = 200t,
KG = 1.7m

Ship’s weight
KG
VM
8800 t6.2m54560tm
(+) 200 load1.7mFinal VM  54900 tm

Final W – 9000 t                                               Final VM  54900 tm

So, we can calculate

Final KG = (Final VM/ Final W)
Final KG = (54900 / 9000)
= 6.1m

Here ‘VM’ stands for vertical moments.

  1. 600 tonnes of cargo were discharged from a vessel from the upper 11m above the keel. In the original KG displacement were 6m and 12600 tonnes, calculate the KG.
Solution:-

Given:-
Weight =12600 t
Original KG =6m
Cargo discharged  = 600 t,

Cargo discharge 11 m above the keel

Ship’s weight
KG
VM
12,600t  6m75,600tm
( -) 600t ( discharge)11m (-) 6600tm

Final Weight =12000 t                               Final VM =69000tm

We know that :

Final KG         =        (Final VM / Final Weight)

Final  KG         =          ( 69,000 / 12000)

= 5.75m

  1. In a vessel of 9900 tonnes displacement and KG 4m, a heavy lift of 100 tonnes is loaded on the UD (KG 15m ). Find the final KG.
Solution:
Ship’s weight
KG
VM
12,600t   4m39,600tm
(+)100 t  load 15m ( +)1500tm

Final W 10000t                                             Final VM =41000tm

We know that:

Final KG         =        (Final VM / Final Weight)
Final KG        =   ( 41000 / 10000 )
=   4.11m.

  1. 500 tonnes of cargo of discharge from the lower the lower hold (KG 3m ) of a vessel whose displacement and KG before discharging were 11500 tonnes and 6.3m . Find the final KG.
Solution:

Given:-

Weight = 11500t
Initial KG = 6.3m
Cargo discharged = 500t, KG =3m

Ship’s weight
KG
VM
11500t 4m39,600tm
(+)100 t  load 15m ( +)1500tm

Final W =11000t                                          Final VM =70950tm

We know that:

Final KG         =        (Final VM / Final Weight)
Final KG         =    (70,950/11000)
=6.45m

  1. 500 tonnes of cargo was shifted 15 meters vertically downwards in a vessel of 10000 tonnes displacement. Find the effect it has on the KG of the vessel and whether KG increases or decreases.
Solution:

Given:-

Weight =10000t,
Cargo shifted downward =500t,

We know that:-

GG1()  = (w x d)/( total weight)
= (500 x 15)/ 10000
=0.75m

Since, The weight is shifted vertically   downward,  the KG of ship will also go down parallel to the KG of the weight

Hence, KG of the ship decrease by 0.75m

  1. In a vessel of 9000 tonnes displacement , KG 10.5m, 300 tonnes of cargo was shifted from the LH (KG 2.5m)to the UDC (KG 11.5m). Find the resultant KG of teh vessel.
Solution :

Weight =9000 t
Original KG = 10.5m ,
Cargo shifted  = 300 t

Vertical Distance of cargo shifted
= (height of UD – height of LH)
= (11.5 -2.5)
= 9m upwards.

Ship’s weight
KG
VM
9000t  10.5m   94500tm
(+)300t 9m(+)2700tm

Final W = 9000                                             Final VM =200t

We know that :

Final KG         =        (Final VM / Final Weight)
Final  KG           = (97200 / 9,000)
= 10.8m.

  1. In a vessel of 9009 tones displacement, KG 8.7m, how many tonnes of cargo can be loaded on the upper deck (KG 15m ) so that the final KG would be comes 9m.
Solution:-

Given:-
Weight = 9009 t,
Original KG =8.7m,

Let cargo loaded be   X   tonnes
Final KG =9m

Ship’s weight
KG
VM
9009 t    8.7m   94500tm
(+) X t (load) 15m(+) (15 X) tm

Final W = (9009 + X) t                 Final VM =(78378.3 + 15X) tm

We know that:

Final KG        =        (Final VM / Final Weight)
Final  KG     = (78378.3 +15X ) /(9009 + X)
9.0         = (78378.3 + 15X)/ (9009+X)
9 x (9009+X)  = (78378.3 + 15X)
(81081 + 9X) =   (15X  + 78378.3)
Hence, 6X    = 78378 .3 – 81081
6X   = 2702.7t
X  = 450.45 t

  1. A heavy lift derrick , whose head is 20m above the keel , is to shift a locomotive weighing 300 tonnes from the UD (KG 8m ) to the LH (KG 2m). If the displacement and initial KG of the vessel were 12000 tonnes and 7.6m, find the KG of the vessels
    1. When the derrick has taken the weight off the UD and
    2. After shifting is over.
Solution:

Given:
Weight = 12000t,
Initial KG =7.6m,
Cargo shifted = 300t,
Change of KG = (8 – 2)
= 6m downwards

Derrick Height = 20m,
KG of the Weight = 8m

(since the weight is on the UD)

Case – 1
Ship’s weight
KG
VM
12000 t     7.6m   91200tm
300t (shift) 12m (+) 3600 tm

Final W =12000 t                                          Final VM =94800tm

We know that:

Final KG        =        (Final VM / Final Weight)
FKG              =          (94800 / 12000)
= 7.9m

Case – 2
Ship’s weight
KG
VM
12000 t     7.6m   91200tm
300t (shift) 6m (-)1800 tm

Final W =12000                               Final VM = 89400tm

We know that:

Final KG        =        (Final VM / Final Weight)
Final  KG         =   (89400 / 12000)
= 7.45m.

  1. On a vessel of 4,950 tonnes displacement, KG 9.2m, the ship’s jumbo derrick is to be load a weight of 50 tonnes from the wharf , on to the UD( KG 8m) . if the head of the derrick is 25m above the keel , calculate the KG of the vessel
    1. when the weight is hanging by the derrick on the centre line but 2m above the UD , and
    2. after loading .
Solution:

Given:-
Weight = 4950t,
Initial KG = 9.2m
Cargo loaded = 50t ,
UD KG =8m
Height of the derrick = 25m

Case – 1
Ship’s weight
KG
VM
4950 t          9.2m     45540 tm
(+) 50t (load)25m   (+) 1250 tm

Final W = 5000t                                    FVM = 46790tm

We know that:

Final KG        =        (Final VM / Final Weight)
Final KG   = (46790 / 5000)
= 9.358m

Case – 2
Ship’s weight
KG
VM
4950 t          9.2m     45540 tm
(+) 50t (load)8m   (+) 400 tm

Final W = 5000t                                      Final VM = 45940tm

We know that:

Final KG        =        (Final VM / Final Weight)
Final KG = (45940 / 5000)
= 9.188m

  1. A ship’s derrick, whose head is 22m above the keel, is used to be discharge a weight of 20 tonnes (KG 5m), lying on the centre line. If the vessel’s displacement and KG before discharging were 6000 tonnes and 8m. Calculate the KG
    1. As soon as the derrick lifts the weight and
    2. After discharging .
Solution:-

Given:-
Weight = 6000t,
Original KG = 8m,
Cargo discharged = 20t,
KG of cargo discharged = 5m
Height of the derrick = 22m

Case – 1
Ship’s weight
KG
VM
6000t  8m      48 000 tm
20t17m  (+) 340 tm

Final W = 6000                                  Final VM    48340 tm

We know that:

Final KG        =        (Final VM / Final Weight)
Final KG = (48340 / 6,000)
= 8.056m

Case – 2
Ship’s weight
KG
VM
6000t  8m      48 000 tm
(-)20t (discharge)   5m  (-) 100 tm

Final W =5980t                                          Final VM = 47900 tm

We know that:

Final KG        =        (Final VM / Final Weight)
Final KG      = (47900/5980)
= 8.010m.

About the author

Amit Sharma

Graduated from M.E.R.I. Mumbai (Mumbai University), After a brief sailing founded this website with the idea to bring the maritime education online which must be free and available for all at all times and to find basic solutions that are of extreme importance to a seafarer by our innovative ideas.