Page 36 - Introduction to Naval Architecture

24 SHIP FORM CALCULATIONS

Figure 3,5

moments of area. Referring to Figure 3.5, these moments about the
y-axis, that is the axis through O, are given by:

First moment = xy dx about the y-axis

2
Second moment = x y dx about the y-axis = I y

The calculations, if done manually, are best set out in tabular form.

Example 3.1

Calculate the area between the curve, defined by the ordinates
below, and the x-axis. Calculate the first and second moments of
area about the x- and y-axes and the position of the centroid of
area.

Solution
There are 9 ordinates spaced one unit apart. The results can be
calculated in tabular fashion as in Table 3.1.
Hence:

29.8
= 9.93 m2