# 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.

**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 :**

**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**

**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:**

**Solution:**

*A**rea* 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.**

**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 :**

**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 = 3200m ^{2}**

**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.**