A ship 120 m long floats at draught of 5.50 m forward and 5.80 m aft ; MCT1 cm 80 tonne m , TPC 13 , LCF 2.5 m forward of midships. Calculate new draught when a mass of 110 tonne is added 24 m aft of midship.
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Given
L = 120 m
df = 5.5 m
da = 5.8 m
MCT1 = 80 t m
TPC = 13
LCF = 2.5 m fwd of midship
m = 110 t
distance = 24 m aft of midship
To find
1. New draught
Solution
Bodily sinkage = mass added / TPC
= m / TPC
= 110 / 13
= 8.461 cm
d = distance the new mass added + LCF
= 24 + 2.5
= 26.5 m
We know that Change in trim, t = Trimming moment / MCT1 cm
= (m x d) / MCT1 cm
= (110 x 26.5) / 80
= 36.44 cm by stern (As weight is added aft)
Distance from LCF to forward, FL = (L/2) - 2.5 (As LCF is fwd)
= (120/2) - 2.5
= 57.5 m
Distance from LCF to aft , WF = (L/2) + 2.5 (As LCF is fwd)
= (120/2) + 2.5
= 62.5 m
Change in trim forward = - (t/L) x FL
= - (36.44/120) x 57.5
= - 17.46 cm
Change in trim aft = + (t/L) x WL
= + (36.44/120) x 62.5
= + 18.98 cm
New draught forward = Initial draught fwd + Bodily sinkage + Change in trim fwd
= 5.5 + 0.0846 - 0.1746
= 5.41 m
New draught aft = Initial draught aft + Bodily sinkage + Change in trim aft
= 5.8 + 0.0846 + 0.1898
= 6.074 m
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