A ship of 8000 tonne displacement has its centre of gravity 4.5 m above the keel and transverse metacentre 5.0 m above the keel when a rectangular tank 7.5 m long and 15 m wide contains sea water. A mass of 10 tonne is moved 12 m across the deck. Calculate the angle of heel: (a) if there is no free surface of water, (b) if the water does not completely fill the tank.

A ship of 8000 tonne displacement has its centre of gravity 4.5 m above the keel and transverse metacentre 5.0 m above the keel when a rectangular tank 7.5 m long and 15 m wide contains sea water. A mass of 10 tonne is moved 12 m across the deck. Calculate the angle of heel:

(a) if there is no free surface of water,

(b) if the water does not completely fill the tank.

Reference: REED'S NAVAL ARCHITECTURE FOR MARINE ENGINEERS (4^th edition), Exercise – 5.10

 

Solution:

a)

GG₁ = w*d/∆

GM = KM – KG = 5 – 4.5 = 0.5 m

 

Tanθ = GG₁/GM

=> Tanθ = w*d/∆*GM

=> Tanθ = 10*12/8000*0.5

=> θ = 1⁰ 43`

B)

I = 1/12 * LB³

  = 1/12 * 7.5* 15³

  = 2109.375

Here, ρ_f = ρ_w

∇ = 8000/1.025

Free surface effect = ρ_f * I/ ρ_w * ∇

                                       = 2109.37 * 1.025/8000

                                       = 0.27 m

GM` = GM – 0.27 = 00.5 – 0.27 = 0.23 m

 

Tan θ = w*d/∆*GM

=> Tan θ = 10*12/8000*0.23

=> θ = 3⁰ 44`