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.
4. 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
5. 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
6. 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.
7. 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
8. 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.
9. 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.
