1. Centroids A centroid is defined as the geometric center of a body. The center of mass is often called the center of gravity and is defined as the location where all the body’s mass or weight can be considered located if it were to be represented as a point mass.

2. CENTROID

4. The centroid of the operating waterplane is the point about which the ship will list and trim. This point is called the center of flotation (F) and it acts as a fulcrum or pivot point for a floating ship.

5. Center of Buoyancy (B) The centroid of the underwater volume of the ship is the location where the resultant buoyant force acts. This point is called the center of buoyancy (B) and is extremely important in static stability calculations. The distance of the center of buoyancy from the centerline of the ship is called the “transverse center of buoyancy” (TCB). The distance of the center of buoyancy from amidships (or the forward or after perpendicular) is called the “longitudinal center of buoyancy” (LCB).

6. Simpson’s 1st Rule Theory Simpson's 1st Rule is used to integrate a curve with an odd number of ordinates evenly spaced along the abscissa Simpson's Rule assumes that the points are connected three at a time by an unknown second order polynomial.

7. Simpson’s 1st Rule Theory

10. Calculation of Waterplane Area

11. Example :The offsets for the 16-ft waterline of a particular ship with five stations are given below. The length between perpendiculars is 326.4 feet. Compute the waterplane area for the sixteen foot waterline.