Ship displacement calculation

Theoretically, the calculation of ship or boat displacement is executed using Simpson's, and, Tzebisheff, or Trapezoidal rules. The most common rule that naval architects use is the Simpson's rule. To understand the basic foundation of the application of Simpson's rule of integration in calculating the areas under curves, please watch the following Youtube video provided by Jennifer Ryan from SNAME.

Naval architects when designing a ship always have to calculate the displacement. The displacement of a ship is the volume of water it displaces when floating. It is the same as the underwater form of the ship and it represents the weight of the ship itself. As the Archimedes law applies, the weight of the displaced water is the same as the weight of the ship.

In the past, the calculation of the ship displacement is a tedious task. Now with the help of a spreadsheet computer application such as Microsoft Excel, or Lotus 123, it can be carried easily provided that all the ordinates of water-planes or sections are readily available from the lines plan drawings.

When I was studying Naval Architecture at the University of Pattimura Ambon in the Maluku islands of Indonesia, the calculation of the ship displacement was done using Simpson's rules.
Simpson integration formulas are well explained in such books as Statics and dynamics of the ship, Basic Ship Theory I. Naval architects use Simpson's rules to calculate the areas of curves of sectional areas, the underwater volume of a ship or boat and many other curve forms. They are not exact rules but they are quite accurate in calculating curve areas. The waterplanes curves which we need to calculate, to obtain the areas and then the volume, are represented by curves defined by Simpson's mathematical equations. This integration calculation is carried out on each waterplane and reintegrated against the draft common intervals to obtain the underwater volume of the ship.

If the calculation approach is done for each sections then we will get what we call as Bonjean curve. Bonjean curve is used not only by naval architects and ship builders but also by ship crews in assessing the displacement of a ship as well as the its center of buoyancy. The vertical and longitudinal center of buoyancy of a ship is needed to assess the metacentric height GM and the righting lever GZ which are two important parameters in the study of ship's stability. by Charles Roring in Manokwari of West Papua.
Also read: Waterplane area calculation using Simpson's rule