Stability 1 – Chapter 7 Final KG

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)	4.2m	3400 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

2. 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 weight	KG	VM
3000 t	3.9m	11700tm
200t (load)	3.0m	(+) 600tm
300t	6.4m	(+) 1920tm
150t	5.2m	(+) 780tm
350t	4m	(+)1400tm

Final W   = 4000 t                                                       Final VM = 16400 tm

We know that:-

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

3. 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 weight	KG	VM
10000t	6.0m	60000 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.

5. 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
2000t	3.66m	7320tm
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

6. 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
3200t	6.2m	19840tm
(+) 5200t (load)	4.8m	(+)24960 tm
(+) X t	10m	(+) 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

7. 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
2600t	4.88m	12688 tm
4600t (load)	5.0m	23000 tm
X t (load)	10m	10X 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.

8. 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
8000t	8.2m	65600tm
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
8000t	8.2m	65600tm
(-)100t	3m	(-)300tm

Final W  = 7900t                                                                Final VM = 65300tm

We know that:-

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

9. 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
15000t	7.9m	118500tm
(+) 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
15000t	7.9m	118500tm
(+ )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.

10. 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
11000t	7.2m	79200tm
(-)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
11000t	7.2m	79200tm
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.