A weight of 12 tonnes, when moved transversely across the deck through a distance of 12m, causes a ship of 4000 tonnes displacement to list 3.8 degrees to starboard. KM 6m. Find the KG.

A weight of 12 tonnes, when moved transversely across the deck through a distance of 12m, causes a ship of 4000 tonnes displacement to list 3.8 degrees to starboard. KM 6m. Find the KG.

Reference: Ship Stability for Masters & Mates (6^th edition), Exercise – 14.5

 

Solution:

GG₁ = w*d/displacement

=> GG₁ = 12*12/4000

=> GG₁ = 0.036 m

 

Tan θ = GG₁/GM

=> GM = GG₁/tanθ

=> GM = 0.036/tan3.8⁰

=> GM = 0.542 m

 

KG = KM – GM = 6 – 0.542 = 5.458 m