A ship 120 metres long, with maximum beam 15m, is floating in salt water at drafts 6.6m F and 7m A. The block coefficient and coefficient of fineness of the water-plane is 0.75. Longitudinal metacentric height 120m. Centre of flotation is amidships. Find how much more cargo can be loaded and in what position relative to amidships if the ship is to cross a bar with a maximum draft of 7m F and A.

A ship 120 metres long, with maximum beam 15m, is floating in salt water at drafts 6.6m F and 7m A. The block coefficient and coefficient of fineness of the water-plane is 0.75. Longitudinal metacentric height 120m. Centre of flotation is amidships. Find how much more cargo can be loaded and in what position relative to amidships if the ship is to cross a bar with a maximum draft of 7m F and A.

Reference: Ship Stability for Masters & Mates (6^th edition), Exercise – 16.18

 

Solution:

Mean draft, d = 7+6.6/2 = 6.5 m

C_b = ∇ / L*B*d

=> 0.75 = ∇ / 120*15*6.5

=> ∇ = 9180 m³

 

MCTC = w*GML/100L

=> MCTC = 9180*1.025*120/100*120

=> MCTC = 94.095 ton-m/cm

C_w = WPA/L*W

=> 0.75 = WPA/120*15

=> WPA = 1350

 

TPC = WPA/97.56

        = 1350/97.56

        = 13.8375 ton-cm

d = L*MCTC/l*TPC

=> d = 120*94.095/60*13.8375

=> d = 13.6 m FOR

 

Let,

‘w’ ton of cargo should be loaded 13.6 m FOR of COF

Bodily sinkage = w/TPC = w/13.8375

New draft = 6.6 + w/13.88375 m

Required draft = 7 m

Change in draft = 7 – 6.6 – w/3.83755 = 0.4 – w/13.83

 

Change in trim = w*d/MCTC

                         = w*13.6/94.05 cm

y/t = L-l/L

=> y/ (13.6w/94.095) = 120-60/120

=> 0.4 – w/13.83 = 13.6w/2*94.095

=> w = 276.75 tons