4 - Ship form calculations

Abstract

This chapter explains the method of ship form calculations required in ship design. The approximate methods of integration are usually adopted, even when computers are employed. These methods rely upon representing the actual hull curves by ones that are defined by simple mathematical equations. An easy way is to draw the shape, the area of which is required, on squared paper and count the squares included within it. If the points at which the parallel lines intersect the area perimeter are joined by straight lines, the area can be represented approximately by the summation of the set of trapezia so formed. The accuracy with which the area under the actual curve is calculated depends upon how closely the straight lines mimic the curve. Many naval architectural calculations are carried out using the Simpson's rules. Simpson's first rule or the 3 ordinate rule can be generalized to any figure defined by an odd number of evenly spaced ordinates and then summing the resulting answers. Odd ordinate Simpson's rules are preferred as they are only marginally less accurate than the next higher even number rule. Even ordinate Tchebycheff rules are also preferred as they are as accurate as the next highest odd ordinate rule.