191.NA July 2022 Q.10

  The following data are available from the hydrostatic curve of a vessel.

Draught (m)	KB (m)	KM(m)	I (m4)
4.9	2.49	10.73	65.25
5.2	2.61	10.79	68.86

 Calculate the TPC at a draught of 5.05 m.

 

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Solution

We know that TPC = (Area of water plane / 100) x Density of water

So first we need to find volume of displacement at 5.2 m draught

We know that BM = I / Vol. of displacement 

BM = I / ▽

▽ = I / BM

     = 65.25 / 8.24             (BM = KM - KB)

     = 7918   at 5.2 m draught

volume of displacement at 4.9 m draught

We know that BM = I / Vol. of displacement 

BM = I / ▽

▽ = I / BM

     = 68.86 / 8.18             (BM = KM - KB)

     = 8418   at 4.9 m draught

Difference in vol of displacement = 8418 - 7918

                                                       = 500

Difference in draught = 5.2 - 4.9

                                   = 0.3

Area of water plane = Diff in vol of displacement / Difference in draught

                                 = 500 / 0.3

                                 = 1666.67 m2

TPC = (1666.67 / 100) x 1.025

        = 17.08