# What is TPC ( Tonnes Per Centimeter )?

The TPC for any given draught is the weight that must be loaded or discharged to change the ship’s mean draught by one centimetre.

A weight of 30 tonnes is loaded on deck so that the mean draught increases by 1 cm

Since the ship’s displacement is equal to the mass of water displaced (Law of Flotation) it follows that the mass of the additional ‘slice’ of displaced water is equal to the added weight of 30 tonnes.

In this instance, 30 tonnes represents the value of the Tonnes per Centimetre Immersion (TPC) for the ship at the initial draught before the weight was loaded.

Derivation of TPC/ how TPC is derived ?

Consider the previous situation.

Since:            Mass = Volume x Density

then:

Mass of additional slice of water = Volume of the additional slice of water X Density.

If the WPA is assumed to not significantly change between the two waterlines, then:

Volume of the slice = WPA (m2) x 1 cm

We cannot multiply m2 by cms, therefore:

Volume of slice = WPA (m2) x 1 (m)/100;

∴ Added displacement (t) = WPA (m2) x 1 (m) x density (t/m3)/100;

Therefore, the formula for TPC is:                       Considering the TPC formula:

It shows that: