22.NA December 2018 Q.7

A ship 90 m long displaces 5200 tonne and floats at draughts of 4.95 m forward and 5.35 
aft when in sea water of 1023 Kg/m³. The waterplane area is 1100m², GM_L 95m, LCB 0.6m 
forward of midships and LCF 2.2m aft of midships. Calculate the new draughts when the 
vessel moves into fresh water of 1002 Kg/m³

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Given 

L = 90 m
Δ = 5200 t
df = 4.95 m
da = 5.35 m
Aw = 1100 m2
GML = 95 m
LCB = 0.6 m fwd of midship
LCF = 2.2 m aft of midship

To find

1.New draught  when the vessel moves into fresh water of 1002 Kg/m³

Solution

MCT1 cm = Δ x GML / 100 x L
                 = (5200 x 95) / (100 x 90)
                 = 54.88 tonne m

Change in mean draught = ((100 x Δ) / Aw) x (୧sw - ୧fw) / (୧sw x ୧fw)
                                     = (100 x 5200) / 1100) x (1.023 - 1.002) / (1.023 x 1.002)
                                     = 9.68 cm increase (As ship goes from SW to FW draught increases)

Distance from LCF to LCB = LCB + LCF (As fwd and aft of midship)
                                     FB = 2.2 + 0.6
                                           = 2.8 m

Change in trim =  (Δ x FB (୧sw - ୧fw)) / (MCT1 cm x ୧sw)
                        = (5200 x 2.8 (1.023 - 1.002)) / (54.88 x 1.023)
                      t = 5.45 cm by head (As ship moves from SW to FW always trim by head)

Draught change FWD = + t/L (L/2 + LCF)
                                    = + 5.45 / 90 x (45 + 2.2)
                                    = + 2.86 cm

Draught change AFT = - t/L (L/2 - LCF)
                                   = - 5.45 / 90 x (45 - 2.2)
                                   = - 2.59 cm

New draught FWD = Initial draught FWD + change in mean draught + draught change FWD
                               = 4.95 + 0.0968 + 0.0286
                               = 5.076 m

New draught AFT = Initial draught AFT + change in mean draught - draught change AFT
                             = 5.35 + 0.0968 - 0.0259
                             = 5.421 m