Hydrostatic curves

We know that the displacement, the position of B, M and F all depends upon the geometry of the underwater hull and can all be calculated for different draughts. It is customary to obtain these quantities for a range of waterplanes parallel to the design waterplane and plot them against draught; draught being measured vertically. Such sets of curves drawn for a particular ship are called Hydrostatic Curves of that ship. 

 Hydrostatic Curves are useful for working out the draughts and the initial stability, as represented by GM, in various conditions of loading. This is done for all normal working conditions of the ship and the Hydrostatic curves thus obtained are available onboard for use. 

    KM is the height of the Metacentre above Keel. KM is dependent upon the draught of the ship. For the given value of KG, we can use the KM obtained from the hydrostatic curves to find the Metacentric Height (GM). For a Cargo ship, the initial GM should not be less than 0.15 meters. The calculation for Hydrostatic Curves 

The hydrostatic particulars of a ship consist of:

Displacement, 

Deadweight, 

Tonnes per centimetre (TPC), 

The height of COB above keel (KB), 

The distance of COB from after perpendicular (AB) or from amidships (HB), 

The height of the transverse metacentre above keel (KMT), 

The height of the longitudinal metacentre above keel (KML), 

The distance of the centre of flotation from after perpendicular (AF) or from amidships (HF), Moment to change trim by one centimetre (MCTC). 

 Since each of these values depends on the draft of the ship, the hydrostatic particulars are given by the shipyard in the form of curves or tables plotted or tabulated against the draft.

 All the hydrostatic curves of a ship may be given, by the shipyard, on a single sheet of graph paper wherein draft may be indicated on the Y-axis and centimetres on the X-axis. For each curve, one centimetre on the X-axis represents a different value. Some shipyards include, on the same graph, Curves of additional information which are dependant on the draft, such as wetted surface area, midship area, block coefficient, water-plane area coefficient, etc. 

 The working will be confined to the construction of one curve at a time.

 When you construct graphs, bear in mind the following points: 

 1. Use the largest scale that will comfortably fit on the paper you have. 

 2 Indicate clearly the scale chosen by you on each axis. 

 3. Draw the €urves to scale on ordinary paper. It is not necessary to use graph paper. 

 4. You need to draw the graphs only within the given limits, for example: if the drafts are given between 2 m and 8 m, it is not normally necessary for you to show drafts less than 2 m or more than 8 m on the graph. 

Hydrostatic Tables

 The hydrostatic particulars of a ship may be given in the form of curves or tables plotted or tabulated against the draft. 

Hydrostatic Draft 

 The hydrostatic particulars of a ship are indicated against the hydrostatic draft which is the true draft of the ship. The hydrostatic draft may be a little different from the amidships draft (which is the arithmetical mean of the drafts fwd and aft) when the ship is not on an even keel. The hydrostatic draft of a ship is the draft measured at the centre of flotation (COF). 

 COF is the geometric centre of the waterplane area of the ship and it is the point about which she would pivot when her trim is changed. The position of COF is indicated by its distance forward of the after perpendicular of the ship (AF) or by its distance forward or abaft midships (HF). AF (or HF, as the case may be) depends on the hydrostatic draft of the ship and its values are indicated against it in the hydrostatic particulars.

In case the COF is situated amidship (i.e. F & H coincident) and some cargo is shifted aft, the change of drafts at the forward and after perpendiculars would be the same in value but opposite in sign but the mean and hydrostatic draught will remain the same.

In case the COF is situated abaft amidships, the change of drafts will still be opposite in sign but the fwd change will be greater and aft draught change would be smaller. The hydrostatic draught will remain the same but the mean draught will reduce.

In case the COF is situated forward of amidships, the change of drafts will still be opposite in sign but the aft change will be greater and the fwd draught change would be smaller. The hydrostatic draught will remain the same but the mean draught will increase.