Ship’s Displacement Calculation using Simpson’s Rule

Before we begin to calculate displacement of a ship, please watch the following video to understand the basic theory of how Simpson's rule is applied in calculating areas of curves.





Displacement of a ship is the volume of sea or fresh water displaced by the ship when floating. The volume of the displaced water is the same as the volume of the immersed hull of the ship. To calculate the volume of the immersed hull, first, we must calculate the several equidistantly spaced waterplane areas from the keel to the designed load waterline. Please, read my previous post on Boat's Waterplane Area Calculation Using Simpson's Rule which I uploaded on this Naval Architecture blog yesterday.

The method for calculating the displacement volume is the same as the one used in waterplane area calculation. All naval architects are familiar with the Simpson's rule. To make my explanation more understandable, I will give a sample of calculation as follows:

A ship is floating at sea at her 4 meters draft. Common interval or CI is 1 meter ( the waterplanes are equidistantly spaced from draft 0 to draft 4 meters). She has waterplane areas and drafts presented as on the following table:


Calculate the ship's displacement in metric ton.
Using Simpson's first rule, the ship's hull volume of immersed in the sea water (mass density = 1.025 ton per cubic meters) is calculated in tabular form as follows:

Ship's volume displacement = 1/3 x C I x total of volume function
= 1/3 x 1 x 7,206 = 2401,999 cubic meters

Because she is floating in sea water her weight = 2401.999 x 1.025 = 2462.049 metric tons

Now, all the design and calculation of ship form can be executed using such computer software as Delftship, and Maxsurf. But how all the ship hydrostatic properties are calculated manually are important to be presented in this blog to help students in naval architects and those who are interested in this field understand the whole philosophy of ship design.  by Charles Roring