Page 38 - statbility for masters and mates

26 Ship Stability for Masters and Mates
Tonnes per Centimetre Immersion (TPC)
The TPC for any draft is the mass which must be loaded or discharged to change a ship's mean draft in salt water by one centimetre, where
TPC water-plane area density of water 100
; TPC WPA r 100
WPA is in m2. r is in t/m3.
Fig. 4.5
Consider a ship ¯oating in salt water at the waterline WL as shown in Figure 4.5. Let `A' be the area of the water-plane in square metres.
Now let a mass of `w' tonnes be loaded so that the mean draft is increased by one centimetre. The ship then ¯oats at the waterline W1 L1. Since the draft has been increased by one centimetre, the mass loaded is equal to the TPC for this draft. Also, since an extra mass of water equal to the mass loaded must be displaced, then the mass of water in the layer between WL and W1 L1 is also equal to the TPC.
Mass Volume Density
A 1 1025tonnes 1:025Atonnes
100 1000 ; TPCsw 1:025A WPA:
TPC in dock water
100
Also, TPCfw WPA 100
100 97:56
Note. When a ship is ¯oating in dock water of a relative density other than 1.025 the weight to be loaded or discharged to change the mean draft by 1 centimetre (TPCdw) may be found from the TPC in salt water (TPCsw) by simple proportion as follows:
or
TPCdw relative density of dock water RDdw TPCsw relative density of salt water RDsw
TPCdw RDdw TPCsw 1:025