Stability 1 – Chapter 4 Solutions

Stability 1 – Chapter 4 Solutions for Exercise 4: Some important terms – displacement; deadweight; form coefficient; reserve buoyancy; Tonnes per centimetre.

1. A box-shaped vessel 120m long and 15m wide has alight draft of 4m and load draft of 9.8m in SW. find her light displacement, load displacement and DWT.

Solution :

Area of box shape vessel = (L x B)
= 120m x 15m
Light draft = 4m

Light displacement = (u/w volume) x ( density)
= (L x b x d )x (1.025)
= (120 x 15 x 4) x (1.025)
= 7380 t

Load draft   = 9.8m

So load displacement = (u/w volume) x (1.025)
= ( L x b x d) x (1.025)
= (120 x 15 x 9.8) x (1.025)
= 18081t

Hence, DWT =   (Load displacement  –  Light displacement)
= ( 18081  –  7380 )
= 10, 701t

2. A box-shaped vessel 100m long and 14m wide is floating in SW at a draft of 7.6m. Her light draft is 3.6 m and load draft 8.5m. Find her present displacement, DWT aboard and DWT available.

Solution:

Area of box shape vessel = (L x B)
= (100m x 14m)

Present draft = 7.6m
Present displacement = (Lx b x d) x (density)
= (100 x 14 x 7.6) x (1.025)
=10906 t
Light draft                = 3.6m

Light displacement = (L x B x D) x(1.025)
= (100 x 14 x 3.6 ) x (1.025)
= 5166t

When Load draft is     = 8.5m

Load displacement = ( L x b x d )x (1.025)
= (100 x 14 x 8.5) x (1.025)
= 12,197.5t

We know that

DWT aboard  =  (present displacement – Light displacement)
=    (10906 t – 5166 t )
= 5740 t

DWT available  = (Load displacement – present displacement)
=   ( 12,197.5 t  – 10,906 t )
= 1291.5t.

3. A ship is 200m long 20m wide at the waterline. If the coefficient of fineness of the water-plane is 0.8, find her TPC in SW, FW and DW of RD 1.015.

Solution :

Given :  (L x B)  = (200m x20) , Cw = 0.8

As we know that :
Cw   =   Area of water plane / ( L x B )
0.8     = Area of water plane / (200 x 20)
(0.8 x 200 x 20) = Water plane area

A   =  3200m²

We can calculate :

TPC in SW = (A/ 100 x 1.025)
= (3200 / 100 x 1.025)
= 32.8 t/cm

TPC in FW   = (A / 100x 1 )
= (3200/100)
= 32 t/cm

TPC in RD of 1.015 =( A /100 x 1.015)
= (3200 /100 x 1.015)
= 32.48 t/cm.

Note : here “A” refers to water plane area.