A box-shaped vessel 55m 7.5m 6m has KG 2.7m, and floats in salt water on an even keel at 4m draft F and A. Calculate the moments of statical stability at (a) 6 degrees heel and (b) 24 degrees heel.

A box-shaped vessel 55m 7.5m 6m has KG 2.7m, and floats in salt water on an even keel at 4m draft F and A. Calculate the moments of statical stability at (a) 6 degrees heel and (b) 24 degrees heel.

Reference: Ship Stability for Masters & Mates (6^th edition), Exercise – 15.5

 

Solution:

a)

w = 55*7.5*4*1.025 = 1691.25 tons

KG = 2.7 m

KB = 0.5*draft = 0.5*4 = 2 m

BM = B²/12d = 7.5²/12*4 = 1.171875 m

KM = KB = BM = 2 + 1.171875 = 3.171875 m

GM = KM – KG = 3.171875 – 2.7 = 0.471875 m

Moment of statical stability = w*GMSinθ

                                              = 1691.25 * 0.47* Sin6⁰

                                              = 83.42 tons-m

b)

Moment of statical stability = w*(GM+0.5BM*Tan²θ) * Sinθ

                                              = 1691.25 * (0.4 + 0.5*1.71*tan24²) * Sin24

                                              = 404.498 tons-m