# Chapter 11- Stability Calculation

Updated: Jun 5, 2020

**1. On a ship of W 5000t , GM 0.3m, 20t was shifted transversely by 5m. Find the list.**

Solution:

W = 5000t, GM = 0.3m, Weight shifted (w) = 20t & d= 5m

Listing moment = (20 x 5 )
= 100tm
** Tanθ = ( Listing Moment) /(W x GM)**
= 100/(5000 x 0.3)
= 3.8 degree.

**2. On a ship of W 8000t, GM 2.0m, If the following transverse shifting were done , find the list:**

**200cargo shifted 4m to stbd****100t cargo shifted 2 m to port****100t cargo shifted 4m to port****50t stores shifted 20m to stbd**

Solution:-

Listing moment due to shifting of cargo
**LM(1) = ( weight x distance )**
= (200 x 4)
= 800 tm (S)

Again, LM (2) = (**Weight x distance** )
= (100 x 2)
= 200 tm (P)

LM(3) = ( **weight x distance** )
= (100 x 4)
= 400 tm (P)

LM(4) = ( **weight x distance** )
= (50 x 20)
= 1000 tm (S)

Final listing moment (LM) = LM(1) + LM(2) +LM(3)+ LM(4) = 800(S) + 200(P) + 400(P) + 1000(S) =1800(S) + 600(P)

So, final listing moments = (1800 – 600) = 1200 tm (S)

Now, **Tanθ** = (**Final LM** )/(**W** x **GM**)
= (1200/(8000 x 2 )
= 4.29 degree (S)

**3. If 200t cargo was shifted downwards by 10m and to starboard by 5m on a ship of W 10000t , KG 7.0m, KM 7.4m, find the list.**

Solution :-

Given : Cargo shifted (w) = 200t, Distance = 10m, d = 5m from CL to stbd W = 10000 t , KG = 7.0m & KM = 7.4m

Final W =10000t Final VM= 68000 tm
** Final KG = (final VM)/ (Final W)**
Final KG = (68000/10000)
= 6.8m

Final **GM= (KM – KG)**
= (7.4 – 6.8)
= 0.6m

Listing moment **(LM) = (weight x distance )**
= (200 x 5)
= 1000tm

**tanθ = LM/(W x GM)**
= 1000 /(10000 x 0.6)
= 9.46 degree

**4. A quantity of grain estimated to be 100t shifts transeversly by 12m and upwards by 1.5m, on a ship of W 12000t , GM 1.2m. Find the list caused.**

Solution:

Grain shifted (w) = 100t, Distance = 12m & transversely, d = 1.5( î) W = 12000 t, GM = 1.2m

**LM caused = (weight x distance)**
= (100 x 12)
= 1200 tm

GG1 (î) =** (distance x weight) /W**
= (1.5 x 100) / 12000
= 0.0125 m

Final GM = (GM – GG1) = (1.2 – 0.0125)m = 1.1875m

**Tanθ = LM /(W x GM )**
= 1200/(12000 x 1.1875)
= 4 degree 8’.

**5. A ship displaces 4950t and has KG 4.85m, KM 5.79m. cargo weighing 50t is loaded 1.25m above the keel and 4m port of the centre line . Find the list**

Solution:

W = 4950 t , KG = 4.85m KM = 5.79m Weight loaded (w) = 50 t KG = 1.25m d = 4 m to CL to port

LM caused = (**weight x distance **)
= (50 x 4)
= 200 tm to port .

Final W = 5000 t Final VM = 24070 tm
Final **KG = (Final VM)/( Final W)**
Final KG = (24070/5000)
= 4.814m

Final **GM = (KM –KG)**
= (5.79 – 4.814) m
= 0.976m.

**Tanθ = LM/(Weight x GM)**
= 200/ (5000 x 0.976)
θ = 2.34 degree

**6. A weight of 100t is discharge from a position 2.45m above the Keel and 6m to port of the centre line of a ship of w 10000t, KM 8.25m, KG 7.45m. Find the list**

Solution:

Weight discharged (w) = 100t, & KG = 2.45m
Transverse distance = 6m to part from CL
W = 10000 t,
KM = 8.25 m,
KG = 7.45m
LM caused = (**weight x distance**)
= (100 x 6) tm
= 600 tm (P)

Final W = 9900 t Final VM = 74255 tm
Final** KG = (Final VM)/ (Final W)**
Final KG = (74255 / 9900)
= 7.5m

Final GM = (KM –KG) = (8.25 – 7.50) m = 0.75m

**Tanθ = LM /( W x GM)**
= 600/(9900 x 0.75)
= 4.62 degree.

**7. A ship of 10000 t displacement, KG 8.3m carries out the following cargo operation:**

If the final KM is 9.6m, find the list.

Solution:

Final W = 9000 t Final VM =81560 tm Final LM = 700(S)

Final** KG = (Final VM)/ (Final W)**
Final KG = (81560 / 9000)
= 9.062 m
** GM = (KM – KG)**
= (9.6 – 9.062)
= 0.538m

**Tanθ = (Final LM)/(final W x GM)**
= (700)/(9000 x 0.538)
= 8.2 degree

**8. A ship of W 9000t, KG 8.3m loads 600t of cargo (KG 4.0m, 3m to port of the centre line ) and discharge 400t of cargo ( KG 9.0m, , from 5m to port of the centre line ). 200t of cargo is then shifted upwards by 5m and to starboard by 8m. 300t of cargo is then is then shifted 1m downwards and 4m port .Find the list if the final KM is 8.95m**.

Solution :

Final W = 9200 t Final VM = 74200 tm FLM = 600(S)

Final **KG = (Final VM)/(Final W)**
Final KG = (74200)/(9200)
= 8.065m

Final** GM = (KM – KG)**
= (8.95 – 8.065)
= 0.885m

tanθ = (600 )/(9200 x 0.885) = 4 degree ( S)

**9. A ship of W 18000 t, KG 7.75m discharge 1500t (6.0m above the keel and 3m port of the centre line ) and loads 500t (10m above the keel and 4m port of the centre line ).**

**Cargo was then shifted as follows ;****500t upwards 2m and to starboard 4m****800 t downwards 2m and to port 3m.**

**If the final KM is 8.935 m, find the list .**

Solution:

Final W = 17000 Final VM = 134900 tm FLM =2100(S)
Final** KG = (Final VM) / (Final W)**
Final KG = (134900/17000)
= 7.935m

Final **GM = (KM –KG)**
= (8.935 – 7.935)
= 1.0 m

We know that :
**Tan θ = Final LM/(Final W x GM)**
= 2100 /(17000 x 1)
= 7 degree 2.6min

**10. A ship listed 8degree to port , displaces 12000t and has KM 7.54m and KG 6.8m . Find how many tonnes of SW ballast must be transfered from NO 2 port DB tank to NO2 stbd DB tank , to up right and vessel , if the tank- centre are 10m apart .**

Solution :

List = 8 degree (P) ,
Displacement (W) = 12000t,
KM = 7.54m &
KG = 6.8m
** GM = (KM – KG)**
= (7.54 – 6.80)
= 0.74m

listing moment** (LM)= (W x GM x tanθ)**
= (12000 x 0.74 x tan80)
= 1248 tm
Listing moment (LM) = (W x D)
1248 tm = (W x 10m)
W =124.8 t

Here to upright the vessel the lighting moment caused on particle must be same at stbd side. So we have to transfer 124.8t of sea water to the stbd side of DB tank to upright the vessel.

**11. A ship displacing 4000t has GM 1.0m (KM 10.0 m and KG 9.0 m) and is listed 10 degree to port .If 16000t of cargo is now loaded on the centre line and the final GM is 1.0m KM 9.0m and KG 8.0m state weather the list would change .if yes , find the new list .**

Solution :

Displacement (W) = 4000t,
GM = 1.0m (initial) ,
list = 10 degree (P)
W = 16000t, G
M = 1.0m (final)
Listing moment** (LM) = (W x GM tanθ)**
= (4000 x 1 x tan 100)
= 705.3 tm

According to question , 16000 t of cargo loaded So Final W = (16000 + 4000) = 20,000t

But, Initial GM = Final GM
Initial LM = Final LM
** Tanθ = (FLM/(W x GM )**
= 705.3/(20000 x 1)
= 2 degree 1 minute ( P).

Hence we can say that,(Yes) list would change due to the loading of cargo.

**12. A ship of W 10000t. GM 1.5m, is listed 5 degree to stbd . If cargo is shifted vertically until her final GM is 0.5m, state whether the list would change . if yes find the new list .**

Solution :

Displacement (W) = 10000t,
GM = 1.5m,
list = 5 degree
Final GM = 0.5m
Listing moment **(LM)= (W x GM tanθ)**
= (10000 x 1.5 x tan50 )
= 1312.33 tm (S)

According to question, cargo shift vertically and now GM becomes 0.5 m
Hence, Due to change of GM , list must be change .
**Tanθ = LM / (W x GM)**
= 1312.33/(10000 x 0.5)
= 14.7dgree stbd

**13. A ship of W 8500t, KM 9.0m, KG 8.3 , is listed 8 to stbd . The following cargo operation were carried out :**

**200 t discharge KG 4m from 5m stbd of CL .****300t discharged KG 5m from 2m port of CL .****100t loaded KG 2m, 4m to stbd of CL .****200t shifted up by 2m and port by 3m.**

**If the final KM is 9.3m , find the final list **.

Solution:

Final W = 8100t Final VM = 68850tm FLM=289.23tm
Final **GM = (Final VM )/(Final W)**
Final KG = (68850 /8100)
= 8.5m

Final **GM = (KM – KG)**
= (9.3 – 8.5)
= 0.8m
** tanθ = Final LM/(W x GM)**
= 289.23/(8100 x 0.8)
= 2degree 33.3minute

**14. A ship of 15000t displacement, KG 8.7m KM 9.5m is listed 10deg to port. The following cargo work was carried out:**

**500t loaded KG 8.0m, 5m stbd of CL .****300t discharged, KG 4.0m, 4 port of CL.**

Find the quantity of SW ballast that must be transferred transversely to bring the vessel up right , the tank centres the being 12m apart.

**NOTE :** Since vessel is required upright , it is not necessary to calculate the final KG or GM unless specifically asked).

Solution:

Displacement (W) = 15000t, KG = 8.7m, KM = 9.5m & list = 10 degree (P) Final W = (15000 + 500) – 300 = 15200 t Initial LM = 15000 x 0.8 x tan 10 = 2115.9 tm (P) Listing moment caused LM(1) = (500 x 5) = 2500 tm (S)

LM (2) = (300 x 4) = 1200 tm (S)

Total listing moment = (2500 + 1200) tm = 3700 tm (S)

According to question and calculation done above , Initial listing moment = 1584.1 tm (S)

So, maintain vessel upright same LM must be created on (P) side. Again, LM = w x d 1584.1 tm = (w x 12) = (1584.1/12) = 132 t

Hence , 132t SW should transferred to (P) side to keel the vessel upright.

**15. A bulk is carrier presently of 12250t, KM 9.8m , KG 9.0m has a list of 6dee to starboard .she then load 1250 t of ore (KG 8m , 2m to stbd of centre line ) and discharges 250t of ore (KG 2m 5m , from star board of centre line). 160t of SW ballast is then transferred from the stbd shoulder tank to the port DB tank vertically downwards by 9m and transversely by 10m ) Find the final list assuming that they are no slack tanks given the final KM is 9.6m **.

Solution:

Final W = 13250t Final VM = 118310 tm FLM =766.57(S)

Final** KG = (Final VM) /(Final W)**
= (118310/13250)
= 8.929 m

Again,

Initial** LM = ( W x GM tanθ)**
= (12250 x 0.8 x tan 6.50)
= 1116.57 (S)

GM = ( KM – KG) = (9.6 – 8.929) = 0.671m

**tanθ = ( Final LM)/( W x GM)**
= (766.57)/( 13250 x 0.671)
= 4.93 degree(S)

**16. From a ship of W 8000t KM 8.6m KG 8.0m some deck cargo was washed overboard KG 10m, 8m from the centre line .if the resultant list is 3 degree, find the quantity of cargo lost.**

Solution:

Final W = (8000 – X) t Final VM =(64000 – 10X)tm
Final **KG = (Final VM)/(Final W)**
= (64000 – 10X)/(8000 –X)

Again, Final GM = (KM – Final KG)
= 8.6 – (64000 – 10X )/(8000 – X)
= 8.6 (8000 -X ) – (64000 – 10X) /(8000 –X)
= (68800 – 8.6X – 64000 + 10X)/(8000 – X)
= (4800 + 1.4X)/(8000 – X)
** Tan θ = (Final LM)/ (Final W x Final GM)**

= 8X / ((8000 – X ) x (4800 + 1.4X)/(8000 –X)) = 8X /(4800 + 1.4X) 8X = tan 30 x (4800 + 1.4X) = (251.56 + 0.073X) (8X – 0 .073X) = 251.56

Hence, X = (251.56/7.927) = 31.73t

**17. A ship of W 16000t, KM 7.5m, KG 6.0m , TPC 25, is listed 3 degree to port .Her present mean draft is 8.6m and she is to finish loading at 8.8m mean draft . Space is available 5m 0f the centre line, on either side. State how much cargo must be stowed on either side to finish upright**

Solution :

W = 16000t, KM, 7.5m KG = 6.0m, Initial GM = 1.5 m TPC = 25, List = 3 degree P Present draft = 8.6m Final draft = 8.8

Sinkage available = (8.8 – 8.6)m = 0.2m = 20cm

Now , Cargo to load = (**Sinkage x TPC**)
= (20 x 25)
= 500 t
** LM =(W x GM tanθ)**

Again , Initial LM = (16000 X 1.5 X Tan 30) = 1257.78 tm

Let ‘X’ t 0f cargo will load on port side Cargo to be load on stbd side = (500 – X) t So, final LM caused due to loading of cargo would be

**LM(1) = (Weight x distance)**
= (X x 5)
= 5X (P)

LM(2) = (Weight x distance) = (500 –X) x 5 = (2500 – 5X ) (S)