It is not feasible to solve the set (1) through (5) as a single problem [1]. Instead, as indicated by experience of designing ships and other complicated objects, the sub-systems should be designed separately. In [1] the actual solution of the problem of obtaining x is defined as follows:

S1, S2  = sub-sets of restrictions represented by strict equations and in equations S  S  S . In [2], [3], the

following equations are applied to the analysis of crane ships (hereinafter abbreviated as CS).

Where = the total displacement of the crane vessel in operational condition; Pi     = a sum of weight loads of



mass groups; M = a design heeling moment [4]; MQ = a maximal loading moment created by cargo on the main hoist

hook of the crane being in operation, [2], [4]; g = acceleration due to gravity; h = the corrected metacentric height (i.e. with consideration of correction for free surfaces); [= the critical value of heeling angle, [4].

Considering the equation C  LBd , the conditions (10), (11) can be re-written as

At early stages, the unknowns are x L, B, d , D,C . = specific gravity of sea water; = sea water density, CB = block coefficient corresponding to the operational state of the crane ship; L, B, d, D = design length, breadth, draft and depth of the ship, respectively.

Thus, according to [1], [2], and [3], the mathematical representation satisfying conditions (12) and (13) is necessary to develop to solve the main problem of crane ship design theory, considering system optimization of that CS. In doing so, certain reliable relations between the main CS’s elements and a number of design parameters  such

as L, B, d , D, C f Q, R, A  , H   , θ should be established as a means of performing practical calculations.

B LD LD

The aim of this article is to build a mathematical representation of the CS based on a number of equations  which

relate the main ship’s elements to her design parameters. In addition, the representation should satisfy conditions

(12) and (13).

When deriving the analytical relations of the main ship’s elements, commonly known relations of ship statics are used in the left-hand side of equations, while some empirical relations specified in Rules [4] are used in the right- hand side of the same equations. When determining coefficients, statistical methods are used. That allows leaving certainly unsuitable candidate solutions out of consideration.

2. Literature – critical overview

A review of the existing approaches, such as [3], [5], [6], [7], [8], indicates that problems of ship theory and hull structure, including some specific issues, are generally solved in designing of vessels under consideration. There are scarcely any publications to reveal the relation between main ship’s elements and principal performances of the CS in terms of solving optimization problems of ship design theory. In addition, many publications have become out of date.

The following drawbacks of the existing publications should be brought to attention:

1. Most comprehensive methods of the determination of CS main elements are intended only for the earliest design stages.

2. In developing general methods (i.e. methods not associated with any highly specialized type of vessel) of the determination of CS main elements, CS’s were being split into no more than two groups, each with its own general and  specific  features,  which were  then allowed  for  in the  principal  equations of the  method  to  obtain vessel’s