Stability – I : Chapter 7

  1. A ship of displacement 2000t and KG 4.2m, loads 300t 0f cargo (KG 2.0m ), 200t of cargo (KG 3.2m) and 500t of bunkers ( KG 0m ). Find her final KG.
Solution:
Ship’s weight
KG
VM
2000t (load)4.2m3400 tm
300t (load)2.0m(+) 600 tm
200t   (load)3.2m(+) 640 tm
500t  (load )1.0 m(+)500 tm

Final W   = 300t                                                           Final VM = 10140 tm

We know that:-

Final KG =   (Final VM) / (Final W)
Final KG    = 10140 / 3000
= 3.38m

  1. A ship of displacement 3000t and KG 3.9m, loads cargo and follows :- 200t in N0.1 LH ( KG 3.0m )300t on the deck ( KG 6.4m ), 150t and NO.3 TD (KG 5.2m ) and 350t in NO.4 LH (KG 4.0m ). Find the final KG .
Solution:
Ship’s weightKGVM
3000 t3.9m11700tm
200t (load)3.0m(+) 600tm
300t6.4m(+) 1920tm
150t5.2m(+) 780tm
350t4m(+)1400tm

Final W   = 4000 t                                                       Final VM = 16400 tm

We know that:-

Final KG =   (Final VM) / (Final W)
Final KG = (16400/4000)
= 4.1m

  1. A ship of load displacement 10,000 t, KG 6.0m, discharge cargo of 250t ( KG 3.0m ) and 150t ( KG 4.0m). Find her final KG.
Solution :
Ship’s weightKGVM
10000t6.0m60000 tm
(-) 250t (discharge)3.0m(-) 750 tm
(-) 150t (discharge)4.0m(-) 600 tm

Final  W  =  9600t                                                 Final  VM = 58650 tm

We know that:-

Final KG =   (Final VM) / (Final W)
Final  KG  = (58650 / 9600)
= 6.109m.

  1. Ship of 2000t displacement of KG 3.66m , loads 1500t( KG5.5m ) 3500t (KG 4.60m ), and takes 1520t of bunkers (KG 0.60m ). She discharge 2000t cargo ( KG 2.44m ). and consume 900t of bunkers ( KG 0.40m ). Find the KG at the and of the voyage.
Solution :
Ship’s   weight
KG
VM
2000t3.66m7320tm
1500t(load)5.5m(+)8250tm
3500t (load)4.60m(+)16100tm
1520t ( load)0.60m(+)912tm
2000t ( discharge)2.44m(-) 4880tm
900t  (discharge)0.40m(-)360tm

Final W   =   5620t                                                    Final VM  = 27342tm

We know that:-

Final KG =   (Final VM) / (Final W)
Final KG = (27342) / (5620)
= 4.865m

  1. A ship of 3200t displacement KG 6.2m , loads 5200t of cargo (KG 4.8 ). Find the amount of deck cargo (KG 10.2m ) that can be loaded so that the KG shall be 6.0m when loading is completed .
Solution:
Ship’s weight
KG
VM
3200t6.2m19840tm
(+) 5200t (load)4.8m(+)24960 tm
(+) X t10m(+) 10X tm

Final W  = (8400 + X )t                                     Final VM   =(44800 +10X);

We know that:-

Final KG =   (Final VM) / (Final W)
6 = (44800 + 10X )/( 8400 + X)
6 (8400 + X  )  = ( 44800 +10X)
(50400 + 6X ) = (10X + 44800)
( 10X – 6X) = (50400 – 44800)
4X = 5600
X  =  1400t

Hence , amount of deck cargo to be loaded to get  required KG is  1400 t

  1. A ship 0f 2600t displacement , KG 4.88m, loads of 4600 t of homogeneous cargo (KG 5.0m ). Find how much deck cargo (KG 10m ) may be loaded to obtain a final KG of 5.11m.
Solution:
Ship’s weight
KG
VM
2600t4.88m12688 tm
4600t (load)5.0m23000 tm
X t (load)10m10X tm

Final W   = (7200 + X) t                                              Final VM =(35688 + 10X) tm

We know that:-

Final KG =   (Final VM) / (Final W)
5.11  =  (35688 + 10X )/( 7200 + X )
5.11( 7200 + X) = (35688 + 10X)
(36792  + 5.11X )  = (35688 +10X)
(36792 – 35688) = (10X – 5.11X )
X  =  1104 / 4.89
X  =225.766t.

Hence amount of deck cargo added to get desired KG is 225.76 t.

  1. A heavy-lift derrick is used to discharge a 100t package from a ship of displacement 8000t kg 8.2m . If the KG  of the weight while on board is 3m and if the derrick head is 25m above the keel , find the kg of the ship  (a) while discharging and( b ) after discharging

Solution :

CASE 1

Ship’s weight
KG
VM
 8000t8.2m65600tm
100t ( while disch)(25 -3m)(+)2200tm

Final W  = 8000t                                                                 Final VM  =  67800t

We know that:-

Final KG =   (Final VM) / (Final W)
Final  KG   =  ( 67800/8000)
=  8.475m

Case – 2

Ship’s weight
KG
VM
8000t8.2m65600tm
(-)100t3m(-)300tm

Final W  = 7900t                                                                Final VM = 65300tm

We know that:-

Final KG =   (Final VM) / (Final W)
Final KG   = (65300/7900)
= 8.266m

  1. On a ship of 15000t displacement kg 7.9m , a weight of 200t is loaded on the UD (KG 12m ) above the Find the KG of the ship (a) while loading , and (b) After loading .
Solution :

Case – 1

Ship’s weight
KG
VM
15000t7.9m118500tm
(+) 200t (while loading)30m(+) 6000tm

Final W  =  15200T                                                           Final  VM  = 124500tm

We know that:-

Final KG =   (Final VM) / (Final W)
Final KG = (124500/15200)
= 8.190m

Case – 2

Ship’s weight
KG
VM
15000t7.9m118500tm
(+ )200t (loaded)12m+2400tm

Final W   =  15200                                                               Final VM = 120900 tm

We know that:-

Final KG =   (Final VM) / (Final W)
Final KG   =   (120900/15200)
=7.954m.

  1. On a ship of 11000 t displacement KG7.2m a shore crane is used to shift a heavy-lift from the UD (KG 12m to the LH (KG 3m ) . Find the kg of the ship (a) during shifting is (b) after shifting .
Solution :

Case -1

Ship’s weight
KG
VM
11000t7.2m79200tm
 (-)180t (while shifting)12m(-)2160tm

Final W =  10820t                                                            Final VM = 77040 tm

We know that:-

Final KG =   (Final VM) / (Final W)
Final KG   = 77040 / 10820
= 7.120m

Case – 2

Ship’s weight
KG
VM
11000t7.2m79200tm
180t (After shift)(12-3)m(-)1620tm

Final  W = 11000                                                        Final VM =   77580tm

We know that:-

Final KG =   (Final VM) / (Final W)
Final KG = (77580/11000)
= 7.053m.

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.

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